internlm/Lean-Github · Datasets at Hugging Face

url stringclasses 147 values	commit stringclasses 147 values	file_path stringlengths 7 101	full_name stringlengths 1 94	start stringlengths 6 10	end stringlengths 6 11	tactic stringlengths 1 11.2k	state_before stringlengths 3 2.09M	state_after stringlengths 6 2.09M
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	simp[TopM.mapDenoteRegion]	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂]) (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	simp[OpM.denoteRegions]	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	simp[Semantics.semantics_op]	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	simp[scf_semantics_op]	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (ite (b = false → False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion r₂ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	cases b <;> simp	r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (ite (b = false → False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion r₂ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)	case false r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) case true r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	case false => { rw[OpM_toTopM_denoteRegion]; simp[TopM.denoteRegionsByIx]; }	r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	case true => { sorry }	r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	rw[OpM_toTopM_denoteRegion]	r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)	r₁ r₂ : Region scf ⊢ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	simp[TopM.denoteRegionsByIx]	r₁ r₂ : Region scf ⊢ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.IF.equivalent	[100, 1]	[149, 10]	sorry	r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.CORRECT_r	[184, 1]	[186, 9]	sorry	n : ℕ r : Region scf args : TypedArgs scf ⊢ run (denoteRegion scf r args) (INPUT n) = Except.ok ([], INPUT n)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.identity₁	[206, 9]	[208, 8]	sorry	n : ℕ ⊢ Int.toNat (Int.ofNat n + 1 - 0) = n + 1	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[LHS, RHS]	n : ℕ r : Region scf ⊢ run ⟦ LHS r ⟧ (INPUT n) = run ⟦ RHS r ⟧ (INPUT n)	n : ℕ r : Region scf ⊢ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteRegion]	n : ℕ r : Region scf ⊢ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)	n : ℕ r : Region scf ⊢ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	n : ℕ r : Region scf ⊢ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)	n : ℕ r : Region scf ⊢ (match run (denoteTypedArgs [] []) (INPUT n) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteTypedArgs_nil]	n : ℕ r : Region scf ⊢ (match run (denoteTypedArgs [] []) (INPUT n) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e	n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOps_singleton]	n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)	n : ℕ r : Region scf ⊢ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOp]	n : ℕ r : Region scf ⊢ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)	n : ℕ r : Region scf ⊢ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	n : ℕ r : Region scf ⊢ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)	n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[INPUT]	n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)	n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOpArgs_cons_]	n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))	n : ℕ r : Region scf ⊢ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	n : ℕ r : Region scf ⊢ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))	n : ℕ r : Region scf ⊢ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[run_TopM_get_]	n : ℕ r : Region scf ⊢ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_ne_val]	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_ne_val]	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_eq_val] <;> simp	n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOpArgs_cons_]	n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[run_TopM_get_]	n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_ne_val]	n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_eq_val] <;> simp	n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOpArgs_nil]	n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_pure]	n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[TopM.mapDenoteRegion]	n : ℕ r : Region scf ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[Semantics.semantics_op, scf_semantics_op]	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[OpM.denoteRegions]	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	apply Eq.symm	n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOps_cons]	case h n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	case h n : ℕ r : Region scf ⊢ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOps_singleton]	case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOp]	case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	case h n : ℕ r : Region scf ⊢ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOpArgs_cons_]	case h n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_bind]	case h n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[run_TopM_get_]	case h n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_ne_val]	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_ne_val]	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	rw[SSAEnv.get_set_eq_val]	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with \| MLIRType.float a => Float \| MLIRType.int signedness sz => FinInt sz \| MLIRType.tensor1d => Tensor1D \| MLIRType.tensor2d => Tensor2D \| MLIRType.tensor4d => Tensor4D \| MLIRType.index => ℤ \| MLIRType.undefined a => Unit \| MLIRType.extended σ => Unit \| MLIRType.erased => Unit) = match MLIRType.index with \| MLIRType.float a => Float \| MLIRType.int signedness sz => FinInt sz \| MLIRType.tensor1d => Tensor1D \| MLIRType.tensor2d => Tensor2D \| MLIRType.tensor4d => Tensor4D \| MLIRType.index => ℤ \| MLIRType.undefined a => Unit \| MLIRType.extended σ => Unit \| MLIRType.erased => Unit) 0) else none with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp	case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with \| MLIRType.float a => Float \| MLIRType.int signedness sz => FinInt sz \| MLIRType.tensor1d => Tensor1D \| MLIRType.tensor2d => Tensor2D \| MLIRType.tensor4d => Tensor4D \| MLIRType.index => ℤ \| MLIRType.undefined a => Unit \| MLIRType.extended σ => Unit \| MLIRType.erased => Unit) = match MLIRType.index with \| MLIRType.float a => Float \| MLIRType.int signedness sz => FinInt sz \| MLIRType.tensor1d => Tensor1D \| MLIRType.tensor2d => Tensor2D \| MLIRType.tensor4d => Tensor4D \| MLIRType.index => ℤ \| MLIRType.undefined a => Unit \| MLIRType.extended σ => Unit \| MLIRType.erased => Unit) 0) else none with \| some v => v \| none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match run (denoteOpArgs scf []) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_denoteOpArgs_nil]	case h n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_pure]	case h n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[TopM_mapDenoteRegion_cons]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[TopM_mapDenoteRegion_nil]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[Semantics.semantics_op, scf_semantics_op]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[OpM_denoteRegions_cons]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[OpM_denoteRegions_nil]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_OpM_toTopM_denoteRegion]	case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp[run_TopM_denoteRegionsByIx_cons]	case h n : ℕ r : Region scf ⊢ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h n : ℕ r : Region scf ⊢ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	sorry	case h n : ℕ r : Region scf ⊢ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with \| Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with \| Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with \| Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') \| Except.error e => Except.error e \| Except.error e => Except.error e with \| Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with \| IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] \| IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] \| IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body \| IOp.mk "scf.yield" resTy vs [] attrs => pure vs \| IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with \| some (AttrValue.str str) => str \| x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] \| IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args \| IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' \| Except.error e => Except.error e \| Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	sorry	case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp	case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Dialects/ScfSemantics.lean	SCF.FOR_PEELING.equivalent	[214, 1]	[270, 2]	simp	case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.all_one	[10, 1]	[12, 20]	simp [all, foldr]	α : Type u_1 P : α → Bool a : α ⊢ all [a] P = true ↔ P a = true	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.ne_mem_cons	[20, 1]	[25, 28]	intros Hne	α : Type u_1 x a : α as : List α ⊢ ¬x ∈ a :: as → x ≠ a ∧ ¬x ∈ as	α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as ⊢ x ≠ a ∧ ¬x ∈ as
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.ne_mem_cons	[20, 1]	[25, 28]	apply And.intro <;> intros _ <;> apply Hne	α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as ⊢ x ≠ a ∧ ¬x ∈ as	case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊢ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.ne_mem_cons	[20, 1]	[25, 28]	. subst x; constructor	case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊢ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as	case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.ne_mem_cons	[20, 1]	[25, 28]	. constructor; assumption	case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	intros α xs	⊢ ∀ {α : Type} (xs : List α) (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs	α : Type xs : List α ⊢ ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	induction xs	α : Type xs : List α ⊢ ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs	case nil α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) [] case cons α : Type head✝ : α tail✝ : List α tail_ih✝ : ∀ (i : ℕ) (INBOUND : i < length tail✝), Mem (getF tail✝ i INBOUND) tail✝ ⊢ ∀ (i : ℕ) (INBOUND : i < length (head✝ :: tail✝)), Mem (getF (head✝ :: tail✝) i INBOUND) (head✝ :: tail✝)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	case nil => { intros i INBOUND; simp at INBOUND; }	α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) []	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	case cons x' xs IH => { intros i INBOUND; cases i; case zero => { simp [List.getF]; constructor; } case succ i' => { simp [List.getF]; constructor; apply IH; } }	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊢ ∀ (i : ℕ) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	intros i INBOUND	α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) []	α : Type i : ℕ INBOUND : i < length [] ⊢ Mem (getF [] i INBOUND) []
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	simp at INBOUND	α : Type i : ℕ INBOUND : i < length [] ⊢ Mem (getF [] i INBOUND) []	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	intros i INBOUND	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊢ ∀ (i : ℕ) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : ℕ INBOUND : i < length (x' :: xs) ⊢ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	cases i	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : ℕ INBOUND : i < length (x' :: xs) ⊢ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)	case zero α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs) case succ α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs n✝ : ℕ INBOUND : Nat.succ n✝ < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ n✝) INBOUND) (x' :: xs)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	case zero => { simp [List.getF]; constructor; }	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	case succ i' => { simp [List.getF]; constructor; apply IH; }	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	simp [List.getF]	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem x' (x' :: xs)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	constructor	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem x' (x' :: xs)	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	simp [List.getF]	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	constructor	α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)	case a α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) xs
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.List.getF_implies_mem	[100, 1]	[120, 2]	apply IH	case a α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) xs	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_uniform	[132, 1]	[133, 45]	induction n <;> simp [uniform]	α : Type u_1 v : α n : ℕ ⊢ length (uniform v n) = n	case succ α : Type u_1 v : α n✝ : ℕ n_ih✝ : length (uniform v n✝) = n✝ ⊢ length (uniform v n✝) = n✝
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_uniform	[132, 1]	[133, 45]	assumption	case succ α : Type u_1 v : α n✝ : ℕ n_ih✝ : length (uniform v n✝) = n✝ ⊢ length (uniform v n✝) = n✝	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_rangeF	[144, 1]	[148, 35]	induction n with \| zero => simp \| succ m ih => simp [rangeF, ih]	n : ℕ ⊢ length (rangeF n) = n	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_rangeF	[144, 1]	[148, 35]	simp	case zero ⊢ length (rangeF Nat.zero) = Nat.zero	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_rangeF	[144, 1]	[148, 35]	simp [rangeF, ih]	case succ m : ℕ ih : length (rangeF m) = m ⊢ length (rangeF (Nat.succ m)) = Nat.succ m	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	simp at h	n i : ℕ h : i < length (rangeF n) ⊢ i < n	n i : ℕ h : i < n ⊢ i < n
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	apply h	n i : ℕ h : i < n ⊢ i < n	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	induction n with \| zero => intro i h; simp; \| succ m ih => intro i exact match i with \| 0 => by simp [getF] \| j+1 => by simp [rangeF, getF, ih]	n : ℕ ⊢ ∀ (i : ℕ) (h : i < length (rangeF n)), getF (rangeF n) i h = { val := i, isLt := (_ : i < n) }	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	intro i h	case zero ⊢ ∀ (i : ℕ) (h : i < length (rangeF Nat.zero)), getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }	case zero i : ℕ h : i < length (rangeF Nat.zero) ⊢ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	simp	case zero i : ℕ h : i < length (rangeF Nat.zero) ⊢ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	intro i	case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } ⊢ ∀ (i : ℕ) (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }	case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	exact match i with \| 0 => by simp [getF] \| j+1 => by simp [rangeF, getF, ih]	case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	simp [getF]	m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : 0 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) 0 h = { val := 0, isLt := (_ : 0 < Nat.succ m) }	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_rangeF	[151, 1]	[161, 42]	simp [rangeF, getF, ih]	m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i j : ℕ ⊢ ∀ (h : j + 1 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) (j + 1) h = { val := j + 1, isLt := (_ : j + 1 < Nat.succ m) }	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.length_remap	[169, 1]	[171, 15]	simp [remap]	α : Type u_1 l : List α f : ℕ → ℕ h : ∀ (n : ℕ), n < length l → f n < length l ⊢ length (remap l f h) = length l	no goals
https://github.com/opencompl/lean-mlir.git	e43d21592801e5e40477b14b7a554e356060c40c	MLIR/Util/List.lean	List.getF_remap	[174, 1]	[177, 15]	apply h_f	α : Type ?u.30674 l : List α f : ℕ → ℕ h_f : ∀ (n : ℕ), n < length l → f n < length l n : ℕ h_n : n < length (remap l f h_f) ⊢ f n < length l	case a α : Type ?u.30674 l : List α f : ℕ → ℕ h_f : ∀ (n : ℕ), n < length l → f n < length l n : ℕ h_n : n < length (remap l f h_f) ⊢ n < length l

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

simp[TopM.mapDenoteRegion]

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂]) (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

simp[OpM.denoteRegions]

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

simp[Semantics.semantics_op]

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

simp[scf_semantics_op]

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion r₂ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (ite (b = false → False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion r₂ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

cases b <;> simp

r₁ r₂ : Region scf b : Bool ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (ite (b = false → False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion r₂ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)

case false r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) case true r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

case false => { rw[OpM_toTopM_denoteRegion]; simp[TopM.denoteRegionsByIx]; }

r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

case true => { sorry }

r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

rw[OpM_toTopM_denoteRegion]

r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₂ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)

r₁ r₂ : Region scf ⊢ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

simp[TopM.denoteRegionsByIx]

r₁ r₂ : Region scf ⊢ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₂ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.IF.equivalent

[100, 1]

[149, 10]

sorry

r₁ r₂ : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf r₂] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.CORRECT_r

[184, 1]

[186, 9]

sorry

n : ℕ r : Region scf args : TypedArgs scf ⊢ run (denoteRegion scf r args) (INPUT n) = Except.ok ([], INPUT n)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.identity₁

[206, 9]

[208, 8]

sorry

n : ℕ ⊢ Int.toNat (Int.ofNat n + 1 - 0) = n + 1

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[LHS, RHS]

n : ℕ r : Region scf ⊢ run ⟦ LHS r ⟧ (INPUT n) = run ⟦ RHS r ⟧ (INPUT n)

n : ℕ r : Region scf ⊢ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteRegion]

n : ℕ r : Region scf ⊢ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)

n : ℕ r : Region scf ⊢ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

n : ℕ r : Region scf ⊢ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

n : ℕ r : Region scf ⊢ (match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteTypedArgs_nil]

n : ℕ r : Region scf ⊢ (match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e

n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOps_singleton]

n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

n : ℕ r : Region scf ⊢ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOp]

n : ℕ r : Region scf ⊢ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

n : ℕ r : Region scf ⊢ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

n : ℕ r : Region scf ⊢ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[INPUT]

n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)

n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOpArgs_cons_]

n : ℕ r : Region scf ⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

n : ℕ r : Region scf ⊢ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

n : ℕ r : Region scf ⊢ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

n : ℕ r : Region scf ⊢ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[run_TopM_get_]

n : ℕ r : Region scf ⊢ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_ne_val]

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_ne_val]

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_eq_val] <;> simp

n : ℕ r : Region scf ⊢ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOpArgs_cons_]

n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[run_TopM_get_]

n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_ne_val]

n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_eq_val] <;> simp

n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOpArgs_nil]

n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_pure]

n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[TopM.mapDenoteRegion]

n : ℕ r : Region scf ⊢ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[Semantics.semantics_op, scf_semantics_op]

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[OpM.denoteRegions]

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

apply Eq.symm

n : ℕ r : Region scf ⊢ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOps_cons]

case h n : ℕ r : Region scf ⊢ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

case h n : ℕ r : Region scf ⊢ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOps_singleton]

case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOp]

case h n : ℕ r : Region scf ⊢ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

case h n : ℕ r : Region scf ⊢ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOpArgs_cons_]

case h n : ℕ r : Region scf ⊢ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_bind]

case h n : ℕ r : Region scf ⊢ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[run_TopM_get_]

case h n : ℕ r : Region scf ⊢ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_ne_val]

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_ne_val]

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

rw[SSAEnv.get_set_eq_val]

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => ℤ | MLIRType.undefined a => Unit | MLIRType.extended σ => Unit | MLIRType.erased => Unit) = match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => ℤ | MLIRType.undefined a => Unit | MLIRType.extended σ => Unit | MLIRType.erased => Unit) 0) else none with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp

case h n : ℕ r : Region scf ⊢ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => ℤ | MLIRType.undefined a => Unit | MLIRType.extended σ => Unit | MLIRType.erased => Unit) = match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => ℤ | MLIRType.undefined a => Unit | MLIRType.extended σ => Unit | MLIRType.erased => Unit) 0) else none with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_denoteOpArgs_nil]

case h n : ℕ r : Region scf ⊢ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_pure]

case h n : ℕ r : Region scf ⊢ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[TopM_mapDenoteRegion_cons]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[TopM_mapDenoteRegion_nil]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[Semantics.semantics_op, scf_semantics_op]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[OpM_denoteRegions_cons]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[OpM_denoteRegions_nil]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_OpM_toTopM_denoteRegion]

case h n : ℕ r : Region scf ⊢ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp[run_TopM_denoteRegionsByIx_cons]

case h n : ℕ r : Region scf ⊢ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h n : ℕ r : Region scf ⊢ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

sorry

case h n : ℕ r : Region scf ⊢ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

sorry

case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp

case h.a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "cn_plus_1" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn_plus_1" ≠ SSAVal.SSAVal "c0" case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Dialects/ScfSemantics.lean

SCF.FOR_PEELING.equivalent

[214, 1]

[270, 2]

simp

case a n : ℕ r : Region scf ⊢ SSAVal.SSAVal "cn" ≠ SSAVal.SSAVal "c0"

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.all_one

[10, 1]

[12, 20]

simp [all, foldr]

α : Type u_1 P : α → Bool a : α ⊢ all [a] P = true ↔ P a = true

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.ne_mem_cons

[20, 1]

[25, 28]

intros Hne

α : Type u_1 x a : α as : List α ⊢ ¬x ∈ a :: as → x ≠ a ∧ ¬x ∈ as

α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as ⊢ x ≠ a ∧ ¬x ∈ as

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.ne_mem_cons

[20, 1]

[25, 28]

apply And.intro <;> intros _ <;> apply Hne

α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as ⊢ x ≠ a ∧ ¬x ∈ as

case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊢ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.ne_mem_cons

[20, 1]

[25, 28]

. subst x; constructor

case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊢ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as

case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.ne_mem_cons

[20, 1]

[25, 28]

. constructor; assumption

case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊢ x ∈ a :: as

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

intros α xs

⊢ ∀ {α : Type} (xs : List α) (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs

α : Type xs : List α ⊢ ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

induction xs

α : Type xs : List α ⊢ ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs

case nil α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) [] case cons α : Type head✝ : α tail✝ : List α tail_ih✝ : ∀ (i : ℕ) (INBOUND : i < length tail✝), Mem (getF tail✝ i INBOUND) tail✝ ⊢ ∀ (i : ℕ) (INBOUND : i < length (head✝ :: tail✝)), Mem (getF (head✝ :: tail✝) i INBOUND) (head✝ :: tail✝)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

case nil => { intros i INBOUND; simp at INBOUND; }

α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) []

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

case cons x' xs IH => { intros i INBOUND; cases i; case zero => { simp [List.getF]; constructor; } case succ i' => { simp [List.getF]; constructor; apply IH; } }

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊢ ∀ (i : ℕ) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

intros i INBOUND

α : Type ⊢ ∀ (i : ℕ) (INBOUND : i < length []), Mem (getF [] i INBOUND) []

α : Type i : ℕ INBOUND : i < length [] ⊢ Mem (getF [] i INBOUND) []

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

simp at INBOUND

α : Type i : ℕ INBOUND : i < length [] ⊢ Mem (getF [] i INBOUND) []

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

intros i INBOUND

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊢ ∀ (i : ℕ) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : ℕ INBOUND : i < length (x' :: xs) ⊢ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

cases i

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : ℕ INBOUND : i < length (x' :: xs) ⊢ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)

case zero α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs) case succ α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs n✝ : ℕ INBOUND : Nat.succ n✝ < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ n✝) INBOUND) (x' :: xs)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

case zero => { simp [List.getF]; constructor; }

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

case succ i' => { simp [List.getF]; constructor; apply IH; }

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

simp [List.getF]

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem x' (x' :: xs)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

constructor

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊢ Mem x' (x' :: xs)

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

simp [List.getF]

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

constructor

α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)

case a α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) xs

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.List.getF_implies_mem

[100, 1]

[120, 2]

apply IH

case a α : Type x' : α xs : List α IH : ∀ (i : ℕ) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : ℕ INBOUND : Nat.succ i' < length (x' :: xs) ⊢ Mem (getF xs i' (_ : i' < length xs)) xs

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_uniform

[132, 1]

[133, 45]

induction n <;> simp [uniform]

α : Type u_1 v : α n : ℕ ⊢ length (uniform v n) = n

case succ α : Type u_1 v : α n✝ : ℕ n_ih✝ : length (uniform v n✝) = n✝ ⊢ length (uniform v n✝) = n✝

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_uniform

[132, 1]

[133, 45]

assumption

case succ α : Type u_1 v : α n✝ : ℕ n_ih✝ : length (uniform v n✝) = n✝ ⊢ length (uniform v n✝) = n✝

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_rangeF

[144, 1]

[148, 35]

induction n with | zero => simp | succ m ih => simp [rangeF, ih]

n : ℕ ⊢ length (rangeF n) = n

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_rangeF

[144, 1]

[148, 35]

simp

case zero ⊢ length (rangeF Nat.zero) = Nat.zero

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_rangeF

[144, 1]

[148, 35]

simp [rangeF, ih]

case succ m : ℕ ih : length (rangeF m) = m ⊢ length (rangeF (Nat.succ m)) = Nat.succ m

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

simp at h

n i : ℕ h : i < length (rangeF n) ⊢ i < n

n i : ℕ h : i < n ⊢ i < n

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

apply h

n i : ℕ h : i < n ⊢ i < n

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

induction n with | zero => intro i h; simp; | succ m ih => intro i exact match i with | 0 => by simp [getF] | j+1 => by simp [rangeF, getF, ih]

n : ℕ ⊢ ∀ (i : ℕ) (h : i < length (rangeF n)), getF (rangeF n) i h = { val := i, isLt := (_ : i < n) }

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

intro i h

case zero ⊢ ∀ (i : ℕ) (h : i < length (rangeF Nat.zero)), getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }

case zero i : ℕ h : i < length (rangeF Nat.zero) ⊢ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

simp

case zero i : ℕ h : i < length (rangeF Nat.zero) ⊢ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

intro i

case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } ⊢ ∀ (i : ℕ) (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }

case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

exact match i with | 0 => by simp [getF] | j+1 => by simp [rangeF, getF, ih]

case succ m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

simp [getF]

m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : ℕ ⊢ ∀ (h : 0 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) 0 h = { val := 0, isLt := (_ : 0 < Nat.succ m) }

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_rangeF

[151, 1]

[161, 42]

simp [rangeF, getF, ih]

m : ℕ ih : ∀ (i : ℕ) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i j : ℕ ⊢ ∀ (h : j + 1 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) (j + 1) h = { val := j + 1, isLt := (_ : j + 1 < Nat.succ m) }

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.length_remap

[169, 1]

[171, 15]

simp [remap]

α : Type u_1 l : List α f : ℕ → ℕ h : ∀ (n : ℕ), n < length l → f n < length l ⊢ length (remap l f h) = length l

no goals

https://github.com/opencompl/lean-mlir.git

e43d21592801e5e40477b14b7a554e356060c40c

MLIR/Util/List.lean

List.getF_remap

[174, 1]

[177, 15]

apply h_f

α : Type ?u.30674 l : List α f : ℕ → ℕ h_f : ∀ (n : ℕ), n < length l → f n < length l n : ℕ h_n : n < length (remap l f h_f) ⊢ f n < length l

case a α : Type ?u.30674 l : List α f : ℕ → ℕ h_f : ∀ (n : ℕ), n < length l → f n < length l n : ℕ h_n : n < length (remap l f h_f) ⊢ n < length l