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/Util/Arith.lean
|
Int.mul_two
|
[39, 1]
|
[44, 22]
|
rw [h]
|
n : β€
h : 2 = 1 + 1
β’ n * 2 = n + n
|
n : β€
h : 2 = 1 + 1
β’ n * (1 + 1) = n + n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_two
|
[39, 1]
|
[44, 22]
|
rw [Int.mul_add]
|
n : β€
h : 2 = 1 + 1
β’ n * (1 + 1) = n + n
|
n : β€
h : 2 = 1 + 1
β’ n * 1 + n * 1 = n + n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_two
|
[39, 1]
|
[44, 22]
|
simp [Int.mul_one]
|
n : β€
h : 2 = 1 + 1
β’ n * 1 + n * 1 = n + n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_zero
|
[48, 1]
|
[48, 45]
|
rfl
|
n : β€
β’ n ^ 0 = 1
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_succ
|
[50, 1]
|
[50, 64]
|
rfl
|
n : β€
m : β
β’ n ^ (m + 1) = n ^ m * n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.two_pow_ge
|
[52, 1]
|
[53, 8]
|
sorry
|
n : β
β’ 2 ^ n β₯ 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.two_pow_pos
|
[55, 1]
|
[56, 8]
|
sorry
|
n : β
β’ 2 ^ n > 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.one_le_two_pow
|
[58, 1]
|
[59, 8]
|
sorry
|
n : β
β’ 1 β€ 2 ^ n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.one_lt_two_pow
|
[61, 1]
|
[62, 8]
|
sorry
|
n : β
β’ n > 0 β 1 < 2 ^ n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mod_bounds
|
[64, 1]
|
[65, 8]
|
sorry
|
a b : β€
β’ a β₯ 0 β a < b β a % b = a
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mod_mod
|
[67, 1]
|
[68, 8]
|
sorry
|
a b : β€
β’ a % b % b = a % b
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mod_ge_neg
|
[70, 1]
|
[71, 8]
|
sorry
|
a b : β€
β’ a % b β₯ -b
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mod_ge
|
[73, 1]
|
[74, 8]
|
sorry
|
a b : β€
β’ a β₯ 0 β a % b β₯ 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mod_lt
|
[76, 1]
|
[77, 8]
|
sorry
|
a b : β€
β’ b > 0 β a % b < b
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.add_mod_right
|
[79, 1]
|
[80, 8]
|
sorry
|
x z : β€
β’ z > 0 β x β₯ 0 β (x + z) % z = x % z
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.add_mod_left
|
[82, 1]
|
[83, 8]
|
sorry
|
x z : β€
β’ z > 0 β x β₯ 0 β (z + x) % z = x % z
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.ge_zero_eq_nonneg
|
[90, 1]
|
[91, 30]
|
simp [GE.ge, LE.le, Int.le]
|
n : β€
β’ n β₯ 0 β NonNeg n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.zero_ge_neg
|
[93, 1]
|
[94, 43]
|
simp [GE.ge, LE.le, Int.le, Int.neg_neg]
|
n : β€
β’ n β₯ 0 β 0 β₯ -n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.add_ge_zero
|
[98, 1]
|
[98, 70]
|
sorry
|
n m : β€
β’ n β₯ 0 β m β₯ 0 β n + m β₯ 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.le_succ
|
[105, 1]
|
[107, 14]
|
suffices NonNeg 1 by simp [LE.le, Int.le, add_sub_assoc, add_sub]; trivial
|
n : β€
β’ n β€ n + 1
|
n : β€
β’ NonNeg 1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.le_succ
|
[105, 1]
|
[107, 14]
|
constructor
|
n : β€
β’ NonNeg 1
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.le_succ
|
[105, 1]
|
[107, 14]
|
simp [LE.le, Int.le, add_sub_assoc, add_sub]
|
n : β€
this : NonNeg 1
β’ n β€ n + 1
|
n : β€
this : NonNeg 1
β’ NonNeg 1
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.le_succ
|
[105, 1]
|
[107, 14]
|
trivial
|
n : β€
this : NonNeg 1
β’ NonNeg 1
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.succ_le_succ
|
[109, 1]
|
[110, 8]
|
sorry
|
n m : β€
β’ n β€ m β n + 1 β€ m + 1
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.ge_trans
|
[112, 1]
|
[115, 23]
|
simp [GE.ge]
|
n k m : β€
β’ n β₯ m β m β₯ k β n β₯ k
|
n k m : β€
β’ m β€ n β k β€ m β k β€ n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.ge_trans
|
[112, 1]
|
[115, 23]
|
intros hβ hβ
|
n k m : β€
β’ m β€ n β k β€ m β k β€ n
|
n k m : β€
hβ : m β€ n
hβ : k β€ m
β’ k β€ n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.ge_trans
|
[112, 1]
|
[115, 23]
|
apply le_trans hβ hβ
|
n k m : β€
hβ : m β€ n
hβ : k β€ m
β’ k β€ n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.lt_add_right
|
[117, 1]
|
[118, 8]
|
sorry
|
n m : β€
β’ m > 0 β n < n + m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_ge_zero
|
[120, 1]
|
[123, 34]
|
rw [Int.ge_zero_eq_nonneg, Int.ge_zero_eq_nonneg, Int.ge_zero_eq_nonneg]
|
n m : β€
β’ n β₯ 0 β m β₯ 0 β n * m β₯ 0
|
n m : β€
β’ NonNeg n β NonNeg m β NonNeg (n * m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_ge_zero
|
[120, 1]
|
[123, 34]
|
intros hn hm
|
n m : β€
β’ NonNeg n β NonNeg m β NonNeg (n * m)
|
n m : β€
hn : NonNeg n
hm : NonNeg m
β’ NonNeg (n * m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_ge_zero
|
[120, 1]
|
[123, 34]
|
cases hn
|
n m : β€
hn : NonNeg n
hm : NonNeg m
β’ NonNeg (n * m)
|
case mk
m : β€
hm : NonNeg m
nβ : β
β’ NonNeg (ofNat nβ * m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_ge_zero
|
[120, 1]
|
[123, 34]
|
cases hm
|
case mk
m : β€
hm : NonNeg m
nβ : β
β’ NonNeg (ofNat nβ * m)
|
case mk.mk
nβΒΉ nβ : β
β’ NonNeg (ofNat nβΒΉ * ofNat nβ)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_ge_zero
|
[120, 1]
|
[123, 34]
|
constructor
|
case mk.mk
nβΒΉ nβ : β
β’ NonNeg (ofNat nβΒΉ * ofNat nβ)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.mul_gt_zero
|
[125, 1]
|
[126, 8]
|
sorry
|
n m : β€
β’ n > 0 β m > 0 β n * m > 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_ge_zero
|
[128, 1]
|
[131, 50]
|
revert n
|
n : β€
m : β
β’ n β₯ 0 β n ^ m β₯ 0
|
m : β
β’ β (n : β€), n β₯ 0 β n ^ m β₯ 0
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_ge_zero
|
[128, 1]
|
[131, 50]
|
induction m <;> intros n h <;> simp
|
m : β
β’ β (n : β€), n β₯ 0 β n ^ m β₯ 0
|
case succ
nβ : β
n_ihβ : β (n : β€), n β₯ 0 β n ^ nβ β₯ 0
n : β€
h : n β₯ 0
β’ 0 β€ n ^ Nat.succ nβ
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_ge_zero
|
[128, 1]
|
[131, 50]
|
case succ acc ih =>
simp [pow_succ]; apply mul_ge_zero (ih _ h) h
|
acc : β
ih : β (n : β€), n β₯ 0 β n ^ acc β₯ 0
n : β€
h : n β₯ 0
β’ 0 β€ n ^ Nat.succ acc
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_ge_zero
|
[128, 1]
|
[131, 50]
|
simp [pow_succ]
|
acc : β
ih : β (n : β€), n β₯ 0 β n ^ acc β₯ 0
n : β€
h : n β₯ 0
β’ 0 β€ n ^ Nat.succ acc
|
acc : β
ih : β (n : β€), n β₯ 0 β n ^ acc β₯ 0
n : β€
h : n β₯ 0
β’ 0 β€ n ^ acc * n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_ge_zero
|
[128, 1]
|
[131, 50]
|
apply mul_ge_zero (ih _ h) h
|
acc : β
ih : β (n : β€), n β₯ 0 β n ^ acc β₯ 0
n : β€
h : n β₯ 0
β’ 0 β€ n ^ acc * n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_gt_zero
|
[133, 1]
|
[136, 50]
|
revert n
|
n : β€
m : β
β’ n > 0 β n ^ m > 0
|
m : β
β’ β (n : β€), n > 0 β n ^ m > 0
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_gt_zero
|
[133, 1]
|
[136, 50]
|
induction m <;> intros n h <;> simp
|
m : β
β’ β (n : β€), n > 0 β n ^ m > 0
|
case succ
nβ : β
n_ihβ : β (n : β€), n > 0 β n ^ nβ > 0
n : β€
h : n > 0
β’ 0 < n ^ Nat.succ nβ
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_gt_zero
|
[133, 1]
|
[136, 50]
|
case succ acc ih =>
simp [pow_succ]; apply mul_gt_zero (ih _ h) h
|
acc : β
ih : β (n : β€), n > 0 β n ^ acc > 0
n : β€
h : n > 0
β’ 0 < n ^ Nat.succ acc
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_gt_zero
|
[133, 1]
|
[136, 50]
|
simp [pow_succ]
|
acc : β
ih : β (n : β€), n > 0 β n ^ acc > 0
n : β€
h : n > 0
β’ 0 < n ^ Nat.succ acc
|
acc : β
ih : β (n : β€), n > 0 β n ^ acc > 0
n : β€
h : n > 0
β’ 0 < n ^ acc * n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.pow_gt_zero
|
[133, 1]
|
[136, 50]
|
apply mul_gt_zero (ih _ h) h
|
acc : β
ih : β (n : β€), n > 0 β n ^ acc > 0
n : β€
h : n > 0
β’ 0 < n ^ acc * n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.lt_add_lt_left
|
[138, 1]
|
[139, 8]
|
sorry
|
n m k : β€
β’ n < m β k + n < k + m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Int.ge_add_ge_right
|
[141, 1]
|
[142, 8]
|
sorry
|
n m k : β€
β’ n β₯ m β n + k β₯ m + k
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Nat.minus_plus_one
|
[150, 1]
|
[151, 26]
|
cases a
|
a : β
h : a > 0
β’ a - 1 + 1 = a
|
case zero
h : zero > 0
β’ zero - 1 + 1 = zero
case succ
nβ : β
h : succ nβ > 0
β’ succ nβ - 1 + 1 = succ nβ
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Nat.minus_plus_one
|
[150, 1]
|
[151, 26]
|
simp at h
|
case zero
h : zero > 0
β’ zero - 1 + 1 = zero
case succ
nβ : β
h : succ nβ > 0
β’ succ nβ - 1 + 1 = succ nβ
|
case succ
nβ : β
h : succ nβ > 0
β’ succ nβ - 1 + 1 = succ nβ
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/Arith.lean
|
Nat.minus_plus_one
|
[150, 1]
|
[151, 26]
|
rfl
|
case succ
nβ : β
h : succ nβ > 0
β’ succ nβ - 1 + 1 = succ nβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_bound
|
[22, 1]
|
[26, 8]
|
intro i h
|
n m : β
β’ β (i : β), i < n * m β transpose_remap n m i < n * m
|
n m i : β
h : i < n * m
β’ transpose_remap n m i < n * m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_bound
|
[22, 1]
|
[26, 8]
|
simp [transpose_remap]
|
n m i : β
h : i < n * m
β’ transpose_remap n m i < n * m
|
n m i : β
h : i < n * m
β’ m * (i % n) + i / n < n * m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_bound
|
[22, 1]
|
[26, 8]
|
sorry
|
n m i : β
h : i < n * m
β’ m * (i % n) + i / n < n * m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_involutive
|
[28, 1]
|
[31, 8]
|
simp [transpose_remap, Function.comp]
|
n m : β
β’ β (i : β), transpose_remap m n (transpose_remap n m i) = i
|
n m : β
β’ β (i : β), n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_involutive
|
[28, 1]
|
[31, 8]
|
intro i
|
n m : β
β’ β (i : β), n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
|
n m i : β
β’ n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_remap_involutive
|
[28, 1]
|
[31, 8]
|
sorry
|
n m i : β
β’ n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
Function.comp_assoc
|
[50, 1]
|
[52, 20]
|
funext x
|
Ξ± : Sort u_1
Ξ² : Sort u_2
Ξ³ : Sort u_3
Ξ΄ : Sort u_4
f : Ξ± β Ξ²
g : Ξ² β Ξ³
h : Ξ³ β Ξ΄
β’ (h β g) β f = h β g β f
|
case h
Ξ± : Sort u_1
Ξ² : Sort u_2
Ξ³ : Sort u_3
Ξ΄ : Sort u_4
f : Ξ± β Ξ²
g : Ξ² β Ξ³
h : Ξ³ β Ξ΄
x : Ξ±
β’ comp (h β g) f x = comp h (g β f) x
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
Function.comp_assoc
|
[50, 1]
|
[52, 20]
|
simp
|
case h
Ξ± : Sort u_1
Ξ² : Sort u_2
Ξ³ : Sort u_3
Ξ΄ : Sort u_4
f : Ξ± β Ξ²
g : Ξ² β Ξ³
h : Ξ³ β Ξ΄
x : Ξ±
β’ comp (h β g) f x = comp h (g β f) x
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_involutive
|
[54, 1]
|
[62, 38]
|
intro t
|
Ξ± n : β
m : MLIR.AST.MLIRTy
β’ β (t : Matrix Ξ± n m), transpose (transpose t) = t
|
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ transpose (transpose t) = t
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_involutive
|
[54, 1]
|
[62, 38]
|
simp [transpose]
|
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ transpose (transpose t) = t
|
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ {
toTensor :=
{ shape := [Ξ±, n],
data :=
List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))),
h_data_size :=
(_ :
List.length
(List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)))) =
shapeProd [Ξ±, n]) },
h_refines :=
(_ :
shapeRefines
{ shape := [Ξ±, n],
data :=
List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data))),
h_data_size :=
(_ :
List.length
(List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)))) =
shapeProd [Ξ±, n]) }.shape
[MLIR.AST.Dimension.Known Ξ±, MLIR.AST.Dimension.Known n] =
true) } =
t
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_involutive
|
[54, 1]
|
[62, 38]
|
apply RankedTensor.eq_of_fields_eq <;> simp
|
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ {
toTensor :=
{ shape := [Ξ±, n],
data :=
List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))),
h_data_size :=
(_ :
List.length
(List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)))) =
shapeProd [Ξ±, n]) },
h_refines :=
(_ :
shapeRefines
{ shape := [Ξ±, n],
data :=
List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data))),
h_data_size :=
(_ :
List.length
(List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β
transpose_remap Ξ± n i < List.length t.toTensor.data)))) =
shapeProd [Ξ±, n]) }.shape
[MLIR.AST.Dimension.Known Ξ±, MLIR.AST.Dimension.Known n] =
true) } =
t
|
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ [Ξ±, n] = t.toTensor.shape
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))) =
t.toTensor.data
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_involutive
|
[54, 1]
|
[62, 38]
|
. rw [βdim_known_project_eq _ t.h_refines] <;> simp
|
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ [Ξ±, n] = t.toTensor.shape
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))) =
t.toTensor.data
|
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))) =
t.toTensor.data
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ToyModel.lean
|
transpose_involutive
|
[54, 1]
|
[62, 38]
|
. simp [List.remap_remap]
apply List.extF <;> simp
simp [transpose_remap_involutive]
|
case a
Ξ± n : β
m : MLIR.AST.MLIRTy
t : Matrix Ξ± n m
β’ List.remap
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ : β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))
(transpose_remap n Ξ±)
(_ :
β (n_1 : β),
n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β), i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data)) β
transpose_remap n Ξ± n_1 <
List.length
(List.remap t.toTensor.data (transpose_remap Ξ± n)
(_ :
β (i : β),
i < List.length t.toTensor.data β transpose_remap Ξ± n i < List.length t.toTensor.data))) =
t.toTensor.data
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.id_map
|
[8, 1]
|
[13, 34]
|
simp [Functor.map]
|
E : Type β Type
R : Type
t : Fitree E R
β’ id <$> t = t
|
E : Type β Type
R : Type
t : Fitree E R
β’ bind t (ret β id) = t
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.id_map
|
[8, 1]
|
[13, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
E : Type β Type
R : Type
t : Fitree E R
β’ bind t (ret β id) = t
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.id_map
|
[8, 1]
|
[13, 34]
|
rfl
|
case Ret
E : Type β Type
R : Type
rβ : R
β’ bind (Ret rβ) (ret β id) = Ret rβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.id_map
|
[8, 1]
|
[13, 34]
|
simp [bind, ih]
|
case Vis
E : Type β Type
R Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E R
ih : β (a : Tβ), bind (kβ a) (ret β id) = kβ a
β’ bind (Vis eβ kβ) (ret β id) = Vis eβ kβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.comp_map
|
[15, 1]
|
[20, 34]
|
simp [Functor.map]
|
Rβ Rβ Rβ : Type
E : Type β Type
f : Rβ β Rβ
g : Rβ β Rβ
t : Fitree E Rβ
β’ (g β f) <$> t = g <$> f <$> t
|
Rβ Rβ Rβ : Type
E : Type β Type
f : Rβ β Rβ
g : Rβ β Rβ
t : Fitree E Rβ
β’ bind t (ret β g β f) = bind t fun x => ret (g (f x))
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.comp_map
|
[15, 1]
|
[20, 34]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih]
|
Rβ Rβ Rβ : Type
E : Type β Type
f : Rβ β Rβ
g : Rβ β Rβ
t : Fitree E Rβ
β’ bind t (ret β g β f) = bind t fun x => ret (g (f x))
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.comp_map
|
[15, 1]
|
[20, 34]
|
rfl
|
case Ret
Rβ Rβ Rβ : Type
E : Type β Type
f : Rβ β Rβ
g : Rβ β Rβ
rβ : Rβ
β’ bind (Ret rβ) (ret β g β f) = bind (Ret rβ) fun x => ret (g (f x))
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.comp_map
|
[15, 1]
|
[20, 34]
|
simp [bind, ih]
|
case Vis
Rβ Rβ Rβ : Type
E : Type β Type
f : Rβ β Rβ
g : Rβ β Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), bind (kβ a) (ret β g β f) = bind (kβ a) fun x => ret (g (f x))
β’ bind (Vis eβ kβ) (ret β g β f) = bind (Vis eβ kβ) fun x => ret (g (f x))
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
simp [SeqLeft.seqLeft, Seq.seq]
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (SeqLeft.seqLeft tβ fun x => tβ) = Seq.seq (Function.const Rβ <$> tβ) fun x => tβ
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (bind tβ fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> tβ) fun y => bind tβ (ret β y)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
induction tβ with
| Ret _ => rfl
| Vis _ _ ih => simp [bind]; funext _; simp [ih]; sorry
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (bind tβ fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> tβ) fun y => bind tβ (ret β y)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
rfl
|
case Ret
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
rβ : Rβ
β’ (bind (Ret rβ) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> Ret rβ) fun y => bind tβ (ret β y)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
simp [bind]
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
β’ (bind (Vis eβ kβ) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> Vis eβ kβ) fun y => bind tβ (ret β y)
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
β’ (fun r => bind (kβ r) fun a => bind tβ fun x => ret a) = fun r =>
bind (kβ r) fun x => bind tβ (ret β Function.const Rβ x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
funext _
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
β’ (fun r => bind (kβ r) fun a => bind tβ fun x => ret a) = fun r =>
bind (kβ r) fun x => bind tβ (ret β Function.const Rβ x)
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (kβ xβ) fun a => bind tβ fun x => ret a) = bind (kβ xβ) fun x => bind tβ (ret β Function.const Rβ x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
simp [ih]
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (kβ xβ) fun a => bind tβ fun x => ret a) = bind (kβ xβ) fun x => bind tβ (ret β Function.const Rβ x)
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (Function.const Rβ <$> kβ xβ) fun y => bind tβ (ret β y)) =
bind (kβ xβ) fun x => bind tβ (ret β Function.const Rβ x)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqLeft_eq
|
[27, 1]
|
[32, 58]
|
sorry
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih :
β (a : Tβ),
(bind (kβ a) fun a => bind tβ fun x => ret a) = bind (Function.const Rβ <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (Function.const Rβ <$> kβ xβ) fun y => bind tβ (ret β y)) =
bind (kβ xβ) fun x => bind tβ (ret β Function.const Rβ x)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
simp [SeqRight.seqRight, Seq.seq]
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (SeqRight.seqRight tβ fun x => tβ) = Seq.seq (Function.const Rβ id <$> tβ) fun x => tβ
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (bind tβ fun x => tβ) = bind (Function.const Rβ id <$> tβ) fun y => bind tβ (ret β y)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
induction tβ with
| Ret _ =>
simp [Function.const, Function.comp, bind]
| Vis _ _ ih =>
simp [bind]; funext _; simp [ih]; sorry
|
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E Rβ
β’ (bind tβ fun x => tβ) = bind (Function.const Rβ id <$> tβ) fun y => bind tβ (ret β y)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
simp [Function.const, Function.comp, bind]
|
case Ret
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
rβ : Rβ
β’ (bind (Ret rβ) fun x => tβ) = bind (Function.const Rβ id <$> Ret rβ) fun y => bind tβ (ret β y)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
simp [bind]
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
β’ (bind (Vis eβ kβ) fun x => tβ) = bind (Function.const Rβ id <$> Vis eβ kβ) fun y => bind tβ (ret β y)
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
β’ (fun r => bind (kβ r) fun x => tβ) = fun r => bind (kβ r) fun x => bind tβ (ret β id)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
funext _
|
case Vis
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
β’ (fun r => bind (kβ r) fun x => tβ) = fun r => bind (kβ r) fun x => bind tβ (ret β id)
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (kβ xβ) fun x => tβ) = bind (kβ xβ) fun x => bind tβ (ret β id)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
simp [ih]
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (kβ xβ) fun x => tβ) = bind (kβ xβ) fun x => bind tβ (ret β id)
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (Function.const Rβ id <$> kβ xβ) fun y => bind tβ (ret β y)) = bind (kβ xβ) fun x => bind tβ (ret β id)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seqRight_eq
|
[34, 1]
|
[41, 44]
|
sorry
|
case Vis.h
E : Type β Type
Rβ Rβ : Type
tβ : Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), (bind (kβ a) fun x => tβ) = bind (Function.const Rβ id <$> kβ a) fun y => bind tβ (ret β y)
xβ : Tβ
β’ (bind (Function.const Rβ id <$> kβ xβ) fun y => bind tβ (ret β y)) = bind (kβ xβ) fun x => bind tβ (ret β id)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.seq_assoc
|
[55, 1]
|
[58, 8]
|
sorry
|
E : Type β Type
Rβ Rβ Rβ : Type
tβ : Fitree E Rβ
tβ : Fitree E (Rβ β Rβ)
tβ : Fitree E (Rβ β Rβ)
β’ (Seq.seq tβ fun x => Seq.seq tβ fun x => tβ) = Seq.seq (Seq.seq (Function.comp <$> tβ) fun x => tβ) fun x => tβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.bind_assoc
|
[81, 1]
|
[86, 31]
|
induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind];
|
E : Type β Type
Rβ Rβ Rβ : Type
t : Fitree E Rβ
kβ : Rβ β Fitree E Rβ
kβ : Rβ β Fitree E Rβ
β’ bind (bind t kβ) kβ = bind t fun x => bind (kβ x) kβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.bind_assoc
|
[81, 1]
|
[86, 31]
|
rfl
|
case Ret
E : Type β Type
Rβ Rβ Rβ : Type
kβ : Rβ β Fitree E Rβ
kβ : Rβ β Fitree E Rβ
rβ : Rβ
β’ bind (bind (Ret rβ) kβ) kβ = bind (Ret rβ) fun x => bind (kβ x) kβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Semantics/FitreeLaws.lean
|
Fitree.bind_assoc
|
[81, 1]
|
[86, 31]
|
simp [bind]
|
case Vis
E : Type β Type
Rβ Rβ Rβ : Type
kβ : Rβ β Fitree E Rβ
kβ : Rβ β Fitree E Rβ
Tβ : Type
eβ : E Tβ
kβ : Tβ β Fitree E Rβ
ih : β (a : Tβ), bind (bind (kβ a) kβ) kβ = bind (kβ a) fun x => bind (kβ x) kβ
β’ bind (bind (Vis eβ kβ) kβ) kβ = bind (Vis eβ kβ) fun x => bind (kβ x) kβ
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
reading/tactic.lean
|
tst3
|
[21, 1]
|
[25, 2]
|
intros h1 h2
|
p q : Prop
β’ p β q β p
|
p q : Prop
h1 : p
h2 : q
β’ p
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
reading/tactic.lean
|
tst3
|
[21, 1]
|
[25, 2]
|
assumption
|
p q : Prop
h1 : p
h2 : q
β’ p
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_ge
|
[40, 1]
|
[46, 8]
|
simp [mod2]
|
a : β€
n : β
β’ mod2 a n β₯ 0
|
a : β€
n : β
β’ 0 β€ a % 2 ^ n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_ge
|
[40, 1]
|
[46, 8]
|
apply Int.mod_ge
|
a : β€
n : β
β’ 0 β€ a % 2 ^ n
|
case a
a : β€
n : β
β’ a β₯ 0
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_ge
|
[40, 1]
|
[46, 8]
|
have h := Int.ge_add_ge_right (2^n) (@Int.mod_ge_neg a (2^n))
|
case a
a : β€
n : β
β’ a β₯ 0
|
case a
a : β€
n : β
h : a % 2 ^ n + 2 ^ n β₯ -2 ^ n + 2 ^ n
β’ a β₯ 0
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_ge
|
[40, 1]
|
[46, 8]
|
rw [Int.add_left_neg] at h
|
case a
a : β€
n : β
h : a % 2 ^ n + 2 ^ n β₯ -2 ^ n + 2 ^ n
β’ a β₯ 0
|
case a
a : β€
n : β
h : a % 2 ^ n + 2 ^ n β₯ 0
β’ a β₯ 0
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_ge
|
[40, 1]
|
[46, 8]
|
sorry
|
case a
a : β€
n : β
h : a % 2 ^ n + 2 ^ n β₯ 0
β’ a β₯ 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_lt
|
[49, 1]
|
[51, 35]
|
simp [mod2]
|
a : β€
n : β
β’ mod2 a n < 2 ^ n
|
a : β€
n : β
β’ a % 2 ^ n < 2 ^ n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_lt
|
[49, 1]
|
[51, 35]
|
apply Int.mod_lt Int.two_pow_pos
|
a : β€
n : β
β’ a % 2 ^ n < 2 ^ n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_idem
|
[56, 1]
|
[60, 34]
|
intros h
|
n : β
a : β€
β’ a β₯ 0 β§ a < 2 ^ n β mod2 a n = a
|
n : β
a : β€
h : a β₯ 0 β§ a < 2 ^ n
β’ mod2 a n = a
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_idem
|
[56, 1]
|
[60, 34]
|
simp [mod2]
|
n : β
a : β€
h : a β₯ 0 β§ a < 2 ^ n
β’ mod2 a n = a
|
n : β
a : β€
h : a β₯ 0 β§ a < 2 ^ n
β’ a % 2 ^ n = a
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.mod2_idem
|
[56, 1]
|
[60, 34]
|
simp [Int.mod_bounds _ h.1 h.2]
|
n : β
a : β€
h : a β₯ 0 β§ a < 2 ^ n
β’ a % 2 ^ n = a
|
no goals
|
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