Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
url
stringclasses
147 values
commit
stringclasses
147 values
file_path
stringlengths
7
101
full_name
stringlengths
1
94
start
stringlengths
6
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end
stringlengths
6
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tactic
stringlengths
1
11.2k
state_before
stringlengths
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2.09M
state_after
stringlengths
6
2.09M
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
intro hneg
κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kvs : List (κ × ν) ⊢ ¬k ∈ map Prod.fst (matchKey kvs k).snd
κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kvs : List (κ × ν) hneg : k ∈ map Prod.fst (matchKey kvs k).snd ⊢ False
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
induction kvs with | nil => cases hneg | cons kv kvs ih => apply ih simp only [matchKey] at hneg cases Decidable.em (kv.fst = k) with | inl heq => simp only [heq, ite_true] at hneg assumption | inr hneq => simp only [hneq, ite_false] at hneg simp only [map] at hneg cases hneg with | head => exact absurd rfl hneq | tail _ h => exact h
κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kvs : List (κ × ν) hneg : k ∈ map Prod.fst (matchKey kvs k).snd ⊢ False
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
cases hneg
case nil κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ hneg : k ∈ map Prod.fst (matchKey [] k).snd ⊢ False
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
apply ih
case cons κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (matchKey (kv :: kvs) k).snd ⊢ False
case cons κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (matchKey (kv :: kvs) k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
simp only [matchKey] at hneg
case cons κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (matchKey (kv :: kvs) k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
case cons κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (if kv.fst = k then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd) else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
cases Decidable.em (kv.fst = k) with | inl heq => simp only [heq, ite_true] at hneg assumption | inr hneq => simp only [hneq, ite_false] at hneg simp only [map] at hneg cases hneg with | head => exact absurd rfl hneq | tail _ h => exact h
case cons κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (if kv.fst = k then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd) else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
simp only [heq, ite_true] at hneg
case cons.inl κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (if kv.fst = k then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd) else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd heq : kv.fst = k ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
case cons.inl κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False heq : kv.fst = k hneg : k ∈ map Prod.fst (matchKey kvs k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
assumption
case cons.inl κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False heq : kv.fst = k hneg : k ∈ map Prod.fst (matchKey kvs k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
simp only [hneq, ite_false] at hneg
case cons.inr κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneg : k ∈ map Prod.fst (if kv.fst = k then (kv.snd :: (matchKey kvs k).fst, (matchKey kvs k).snd) else ((matchKey kvs k).fst, (kv.fst, kv.snd) :: (matchKey kvs k).snd)).snd hneq : ¬kv.fst = k ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
case cons.inr κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneq : ¬kv.fst = k hneg : k ∈ map Prod.fst ((kv.fst, kv.snd) :: (matchKey kvs k).snd) ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
simp only [map] at hneg
case cons.inr κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneq : ¬kv.fst = k hneg : k ∈ map Prod.fst ((kv.fst, kv.snd) :: (matchKey kvs k).snd) ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
case cons.inr κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneq : ¬kv.fst = k hneg : k ∈ kv.fst :: map Prod.fst (matchKey kvs k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
cases hneg with | head => exact absurd rfl hneq | tail _ h => exact h
case cons.inr κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneq : ¬kv.fst = k hneg : k ∈ kv.fst :: map Prod.fst (matchKey kvs k).snd ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
exact absurd rfl hneq
case cons.inr.head κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ kv : κ × ν kvs : List (κ × ν) ih : kv.fst ∈ map Prod.fst (matchKey kvs kv.fst).snd → False hneq : ¬kv.fst = kv.fst ⊢ kv.fst ∈ map Prod.fst (matchKey kvs kv.fst).snd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.not_mem_matchKey_self_map_snd
[857, 1]
[875, 28]
exact h
case cons.inr.tail κ : Type u_1 ν : Type u_2 inst✝ : DecidableEq κ k : κ kv : κ × ν kvs : List (κ × ν) ih : k ∈ map Prod.fst (matchKey kvs k).snd → False hneq : ¬kv.fst = k h : Mem k (map Prod.fst (matchKey kvs k).snd) ⊢ k ∈ map Prod.fst (matchKey kvs k).snd
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.fst_mem_of_pair_mem
[877, 1]
[881, 80]
contradiction
α : Type u_1 β : Type u_2 x : α y : β hxy : (x, y) ∈ [] ⊢ x ∈ map Prod.fst []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
rw [reverse_eq_reverseSpec]
α : Type u_1 x : α xs : List α ⊢ x ∈ xs ↔ x ∈ reverse xs
α : Type u_1 x : α xs : List α ⊢ x ∈ xs ↔ x ∈ reverseSpec xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
apply Iff.intro
α : Type u_1 x : α xs : List α ⊢ x ∈ xs ↔ x ∈ reverseSpec xs
case mp α : Type u_1 x : α xs : List α ⊢ x ∈ xs → x ∈ reverseSpec xs case mpr α : Type u_1 x : α xs : List α ⊢ x ∈ reverseSpec xs → x ∈ xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
. intro hf induction hf with | head xs => simp only [reverseSpec] apply mem_append_singleton | @tail y ys h_x_ys ih => simp only [reverseSpec] apply mem_append_front _ _ _ ih
case mp α : Type u_1 x : α xs : List α ⊢ x ∈ xs → x ∈ reverseSpec xs case mpr α : Type u_1 x : α xs : List α ⊢ x ∈ reverseSpec xs → x ∈ xs
case mpr α : Type u_1 x : α xs : List α ⊢ x ∈ reverseSpec xs → x ∈ xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
. intro hb induction xs with | nil => contradiction | cons y ys ih => simp only [reverseSpec] at hb rw [List.mem_append_comm] at hb simp only [HAppend.hAppend, Append.append, List.append] at hb cases hb with | head => exact Mem.head _ | tail _ htail => exact Mem.tail _ (ih htail)
case mpr α : Type u_1 x : α xs : List α ⊢ x ∈ reverseSpec xs → x ∈ xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
intro hf
case mp α : Type u_1 x : α xs : List α ⊢ x ∈ xs → x ∈ reverseSpec xs
case mp α : Type u_1 x : α xs : List α hf : x ∈ xs ⊢ x ∈ reverseSpec xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
induction hf with | head xs => simp only [reverseSpec] apply mem_append_singleton | @tail y ys h_x_ys ih => simp only [reverseSpec] apply mem_append_front _ _ _ ih
case mp α : Type u_1 x : α xs : List α hf : x ∈ xs ⊢ x ∈ reverseSpec xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
simp only [reverseSpec]
case mp.head α : Type u_1 x : α xs✝ xs : List α ⊢ x ∈ reverseSpec (x :: xs)
case mp.head α : Type u_1 x : α xs✝ xs : List α ⊢ x ∈ reverseSpec xs ++ [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
apply mem_append_singleton
case mp.head α : Type u_1 x : α xs✝ xs : List α ⊢ x ∈ reverseSpec xs ++ [x]
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
simp only [reverseSpec]
case mp.tail α : Type u_1 x : α xs : List α y : α ys : List α h_x_ys : Mem x ys ih : x ∈ reverseSpec ys ⊢ x ∈ reverseSpec (y :: ys)
case mp.tail α : Type u_1 x : α xs : List α y : α ys : List α h_x_ys : Mem x ys ih : x ∈ reverseSpec ys ⊢ x ∈ reverseSpec ys ++ [y]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
apply mem_append_front _ _ _ ih
case mp.tail α : Type u_1 x : α xs : List α y : α ys : List α h_x_ys : Mem x ys ih : x ∈ reverseSpec ys ⊢ x ∈ reverseSpec ys ++ [y]
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
intro hb
case mpr α : Type u_1 x : α xs : List α ⊢ x ∈ reverseSpec xs → x ∈ xs
case mpr α : Type u_1 x : α xs : List α hb : x ∈ reverseSpec xs ⊢ x ∈ xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
induction xs with | nil => contradiction | cons y ys ih => simp only [reverseSpec] at hb rw [List.mem_append_comm] at hb simp only [HAppend.hAppend, Append.append, List.append] at hb cases hb with | head => exact Mem.head _ | tail _ htail => exact Mem.tail _ (ih htail)
case mpr α : Type u_1 x : α xs : List α hb : x ∈ reverseSpec xs ⊢ x ∈ xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
contradiction
case mpr.nil α : Type u_1 x : α hb : x ∈ reverseSpec [] ⊢ x ∈ []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
simp only [reverseSpec] at hb
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ reverseSpec (y :: ys) ⊢ x ∈ y :: ys
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ reverseSpec ys ++ [y] ⊢ x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
rw [List.mem_append_comm] at hb
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ reverseSpec ys ++ [y] ⊢ x ∈ y :: ys
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ [y] ++ reverseSpec ys ⊢ x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
simp only [HAppend.hAppend, Append.append, List.append] at hb
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ [y] ++ reverseSpec ys ⊢ x ∈ y :: ys
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ y :: reverseSpec ys ⊢ x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
cases hb with | head => exact Mem.head _ | tail _ htail => exact Mem.tail _ (ih htail)
case mpr.cons α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys hb : x ∈ y :: reverseSpec ys ⊢ x ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
exact Mem.head _
case mpr.cons.head α : Type u_1 x : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys ⊢ x ∈ x :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_reverse_iff
[946, 1]
[967, 52]
exact Mem.tail _ (ih htail)
case mpr.cons.tail α : Type u_1 x y : α ys : List α ih : x ∈ reverseSpec ys → x ∈ ys htail : Mem x (reverseSpec ys) ⊢ x ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
simp only [all]
α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (all xs fun x => decide (p x)) = true ↔ ∀ (x : α), x ∈ xs → p x
α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ foldr (fun a r => decide (p a) && r) true xs = true ↔ ∀ (x : α), x ∈ xs → p x
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply Iff.intro
α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ foldr (fun a r => decide (p a) && r) true xs = true ↔ ∀ (x : α), x ∈ xs → p x
case mp α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ foldr (fun a r => decide (p a) && r) true xs = true → ∀ (x : α), x ∈ xs → p x case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
. intros hforward x hx induction hx with | head as => simp [foldr] at hforward apply And.left hforward | tail a h ih => apply ih simp [foldr] at hforward apply And.right hforward
case mp α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ foldr (fun a r => decide (p a) && r) true xs = true → ∀ (x : α), x ∈ xs → p x case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true
case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
. intros hbackward induction xs with | nil => simp [foldr] | cons x xs ih => simp [foldr] apply And.intro . apply hbackward x (List.Mem.head _) . apply ih intro x' hx' apply hbackward _ $ List.Mem.tail _ hx'
case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
intros hforward x hx
case mp α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ foldr (fun a r => decide (p a) && r) true xs = true → ∀ (x : α), x ∈ xs → p x
case mp α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α hforward : foldr (fun a r => decide (p a) && r) true xs = true x : α hx : x ∈ xs ⊢ p x
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
induction hx with | head as => simp [foldr] at hforward apply And.left hforward | tail a h ih => apply ih simp [foldr] at hforward apply And.right hforward
case mp α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α hforward : foldr (fun a r => decide (p a) && r) true xs = true x : α hx : x ∈ xs ⊢ p x
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
simp [foldr] at hforward
case mp.head α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x : α as : List α hforward : foldr (fun a r => decide (p a) && r) true (x :: as) = true ⊢ p x
case mp.head α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x : α as : List α hforward : p x ∧ foldr (fun a r => decide (p a) && r) true as = true ⊢ p x
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply And.left hforward
case mp.head α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x : α as : List α hforward : p x ∧ foldr (fun a r => decide (p a) && r) true as = true ⊢ p x
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply ih
case mp.tail α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x a : α as✝ : List α h : Mem x as✝ ih : foldr (fun a r => decide (p a) && r) true as✝ = true → p x hforward : foldr (fun a r => decide (p a) && r) true (a :: as✝) = true ⊢ p x
case mp.tail α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x a : α as✝ : List α h : Mem x as✝ ih : foldr (fun a r => decide (p a) && r) true as✝ = true → p x hforward : foldr (fun a r => decide (p a) && r) true (a :: as✝) = true ⊢ foldr (fun a r => decide (p a) && r) true as✝ = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
simp [foldr] at hforward
case mp.tail α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x a : α as✝ : List α h : Mem x as✝ ih : foldr (fun a r => decide (p a) && r) true as✝ = true → p x hforward : foldr (fun a r => decide (p a) && r) true (a :: as✝) = true ⊢ foldr (fun a r => decide (p a) && r) true as✝ = true
case mp.tail α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x a : α as✝ : List α h : Mem x as✝ ih : foldr (fun a r => decide (p a) && r) true as✝ = true → p x hforward : p a ∧ foldr (fun a r => decide (p a) && r) true as✝ = true ⊢ foldr (fun a r => decide (p a) && r) true as✝ = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply And.right hforward
case mp.tail α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α x a : α as✝ : List α h : Mem x as✝ ih : foldr (fun a r => decide (p a) && r) true as✝ = true → p x hforward : p a ∧ foldr (fun a r => decide (p a) && r) true as✝ = true ⊢ foldr (fun a r => decide (p a) && r) true as✝ = true
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
intros hbackward
case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α ⊢ (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true
case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α hbackward : ∀ (x : α), x ∈ xs → p x ⊢ foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
induction xs with | nil => simp [foldr] | cons x xs ih => simp [foldr] apply And.intro . apply hbackward x (List.Mem.head _) . apply ih intro x' hx' apply hbackward _ $ List.Mem.tail _ hx'
case mpr α : Type u_1 p : α → Prop inst✝ : DecidablePred p xs : List α hbackward : ∀ (x : α), x ∈ xs → p x ⊢ foldr (fun a r => decide (p a) && r) true xs = true
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
simp [foldr]
case mpr.nil α : Type u_1 p : α → Prop inst✝ : DecidablePred p hbackward : ∀ (x : α), x ∈ [] → p x ⊢ foldr (fun a r => decide (p a) && r) true [] = true
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
simp [foldr]
case mpr.cons α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true (x :: xs) = true
case mpr.cons α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ p x ∧ foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply And.intro
case mpr.cons α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ p x ∧ foldr (fun a r => decide (p a) && r) true xs = true
case mpr.cons.left α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ p x case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
. apply hbackward x (List.Mem.head _)
case mpr.cons.left α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ p x case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true xs = true
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true xs = true
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
. apply ih intro x' hx' apply hbackward _ $ List.Mem.tail _ hx'
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true xs = true
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply hbackward x (List.Mem.head _)
case mpr.cons.left α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ p x
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply ih
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ foldr (fun a r => decide (p a) && r) true xs = true
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ ∀ (x : α), x ∈ xs → p x
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
intro x' hx'
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 ⊢ ∀ (x : α), x ∈ xs → p x
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 x' : α hx' : x' ∈ xs ⊢ p x'
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.all_pred
[1004, 1]
[1026, 48]
apply hbackward _ $ List.Mem.tail _ hx'
case mpr.cons.right α : Type u_1 p : α → Prop inst✝ : DecidablePred p x : α xs : List α ih : (∀ (x : α), x ∈ xs → p x) → foldr (fun a r => decide (p a) && r) true xs = true hbackward : ∀ (x_1 : α), x_1 ∈ x :: xs → p x_1 x' : α hx' : x' ∈ xs ⊢ p x'
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
apply Iff.intro
α : Type u_1 y : α ys : List α x : α ⊢ x ∈ y :: ys ↔ x ∈ [y] ∨ x ∈ ys
case mp α : Type u_1 y : α ys : List α x : α ⊢ x ∈ y :: ys → x ∈ [y] ∨ x ∈ ys case mpr α : Type u_1 y : α ys : List α x : α ⊢ x ∈ [y] ∨ x ∈ ys → x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
. intro hf cases hf with | head => apply Or.intro_left _ (Mem.head _) | tail _ h => apply Or.intro_right _ h
case mp α : Type u_1 y : α ys : List α x : α ⊢ x ∈ y :: ys → x ∈ [y] ∨ x ∈ ys case mpr α : Type u_1 y : α ys : List α x : α ⊢ x ∈ [y] ∨ x ∈ ys → x ∈ y :: ys
case mpr α : Type u_1 y : α ys : List α x : α ⊢ x ∈ [y] ∨ x ∈ ys → x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
. intro hb cases hb with | inl h => rw [(mem_singleton_iff x y).mp h]; apply Mem.head | inr h => apply Mem.tail _ h
case mpr α : Type u_1 y : α ys : List α x : α ⊢ x ∈ [y] ∨ x ∈ ys → x ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
intro hf
case mp α : Type u_1 y : α ys : List α x : α ⊢ x ∈ y :: ys → x ∈ [y] ∨ x ∈ ys
case mp α : Type u_1 y : α ys : List α x : α hf : x ∈ y :: ys ⊢ x ∈ [y] ∨ x ∈ ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
cases hf with | head => apply Or.intro_left _ (Mem.head _) | tail _ h => apply Or.intro_right _ h
case mp α : Type u_1 y : α ys : List α x : α hf : x ∈ y :: ys ⊢ x ∈ [y] ∨ x ∈ ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
apply Or.intro_left _ (Mem.head _)
case mp.head α : Type u_1 y : α ys : List α ⊢ y ∈ [y] ∨ y ∈ ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
apply Or.intro_right _ h
case mp.tail α : Type u_1 y : α ys : List α x : α h : Mem x ys ⊢ x ∈ [y] ∨ x ∈ ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
intro hb
case mpr α : Type u_1 y : α ys : List α x : α ⊢ x ∈ [y] ∨ x ∈ ys → x ∈ y :: ys
case mpr α : Type u_1 y : α ys : List α x : α hb : x ∈ [y] ∨ x ∈ ys ⊢ x ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
cases hb with | inl h => rw [(mem_singleton_iff x y).mp h]; apply Mem.head | inr h => apply Mem.tail _ h
case mpr α : Type u_1 y : α ys : List α x : α hb : x ∈ [y] ∨ x ∈ ys ⊢ x ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
rw [(mem_singleton_iff x y).mp h]
case mpr.inl α : Type u_1 y : α ys : List α x : α h : x ∈ [y] ⊢ x ∈ y :: ys
case mpr.inl α : Type u_1 y : α ys : List α x : α h : x ∈ [y] ⊢ y ∈ y :: ys
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
apply Mem.head
case mpr.inl α : Type u_1 y : α ys : List α x : α h : x ∈ [y] ⊢ y ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.mem_cons_iff_mem_singleton_or_tail
[1040, 1]
[1050, 34]
apply Mem.tail _ h
case mpr.inr α : Type u_1 y : α ys : List α x : α h : x ∈ ys ⊢ x ∈ y :: ys
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
rw [filter_eq_filterSpec, filter_eq_filterSpec, filter_eq_filterSpec]
α : Type u_1 p₁ p₂ : α → Bool xs : List α ⊢ filter p₁ (filter p₂ xs) = filter (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
α : Type u_1 p₁ p₂ : α → Bool xs : List α ⊢ filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
induction xs with | nil => simp [filterSpec] | cons x xs ih => cases h₂ : p₂ x with | false => simp only [filterSpec, h₂, ite_false] exact ih | true => simp only [filterSpec, h₂, ite_true] cases h₁ : p₁ x with | false => simp only [filterSpec, h₁, h₂, ite_false] exact ih | true => simp only [filterSpec, h₁, h₂, ite_true] exact congrArg _ ih
α : Type u_1 p₁ p₂ : α → Bool xs : List α ⊢ filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
simp [filterSpec]
case nil α : Type u_1 p₁ p₂ : α → Bool ⊢ filterSpec p₁ (filterSpec p₂ []) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) []
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
cases h₂ : p₂ x with | false => simp only [filterSpec, h₂, ite_false] exact ih | true => simp only [filterSpec, h₂, ite_true] cases h₁ : p₁ x with | false => simp only [filterSpec, h₁, h₂, ite_false] exact ih | true => simp only [filterSpec, h₁, h₂, ite_true] exact congrArg _ ih
case cons α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs ⊢ filterSpec p₁ (filterSpec p₂ (x :: xs)) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) (x :: xs)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
simp only [filterSpec, h₂, ite_false]
case cons.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = false ⊢ filterSpec p₁ (filterSpec p₂ (x :: xs)) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) (x :: xs)
case cons.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = false ⊢ filterSpec p₁ (filterSpec p₂ xs) = if decide (False ∧ p₁ x = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
exact ih
case cons.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = false ⊢ filterSpec p₁ (filterSpec p₂ xs) = if decide (False ∧ p₁ x = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
simp only [filterSpec, h₂, ite_true]
case cons.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true ⊢ filterSpec p₁ (filterSpec p₂ (x :: xs)) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) (x :: xs)
case cons.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true ⊢ (if p₁ x = true then x :: filterSpec p₁ (filterSpec p₂ xs) else filterSpec p₁ (filterSpec p₂ xs)) = if decide (True ∧ p₁ x = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
cases h₁ : p₁ x with | false => simp only [filterSpec, h₁, h₂, ite_false] exact ih | true => simp only [filterSpec, h₁, h₂, ite_true] exact congrArg _ ih
case cons.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true ⊢ (if p₁ x = true then x :: filterSpec p₁ (filterSpec p₂ xs) else filterSpec p₁ (filterSpec p₂ xs)) = if decide (True ∧ p₁ x = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
simp only [filterSpec, h₁, h₂, ite_false]
case cons.true.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = false ⊢ (if false = true then x :: filterSpec p₁ (filterSpec p₂ xs) else filterSpec p₁ (filterSpec p₂ xs)) = if decide (True ∧ false = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
case cons.true.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = false ⊢ filterSpec p₁ (filterSpec p₂ xs) = if decide (True ∧ False) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
exact ih
case cons.true.false α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = false ⊢ filterSpec p₁ (filterSpec p₂ xs) = if decide (True ∧ False) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
simp only [filterSpec, h₁, h₂, ite_true]
case cons.true.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = true ⊢ (if true = true then x :: filterSpec p₁ (filterSpec p₂ xs) else filterSpec p₁ (filterSpec p₂ xs)) = if decide (True ∧ true = true) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
case cons.true.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = true ⊢ x :: filterSpec p₁ (filterSpec p₂ xs) = if decide (True ∧ True) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.filter_filter
[1055, 1]
[1073, 28]
exact congrArg _ ih
case cons.true.true α : Type u_1 p₁ p₂ : α → Bool x : α xs : List α ih : filterSpec p₁ (filterSpec p₂ xs) = filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs h₂ : p₂ x = true h₁ : p₁ x = true ⊢ x :: filterSpec p₁ (filterSpec p₂ xs) = if decide (True ∧ True) = true then x :: filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs else filterSpec (fun x => decide (p₂ x = true ∧ p₁ x = true)) xs
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp [uniqueAux, reverse, reverseAux, unique]
α : Type u_1 inst✝ : DecidableEq α acc : List α ⊢ uniqueAux [] acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) [])
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [uniqueAux, filter]
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) ⊢ uniqueAux (x :: xs) acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) (x :: xs))
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) ⊢ (if x ∈ acc then uniqueAux xs acc else uniqueAux xs (x :: acc)) = reverse acc ++ unique (match decide ¬x ∈ acc with | true => x :: filter (fun x => decide ¬x ∈ acc) xs | false => filter (fun x => decide ¬x ∈ acc) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
cases Decidable.em (x ∈ acc) with | inl hin => simp only [hin, ite_true, not_true_eq_false, decide_False] rw [ih₁] | inr hout => simp only [hout, ite_false, not_false_eq_true, decide_True] simp only [reverse_singleton, singleton_append, unique, uniqueAux, List.not_mem_nil, ite_false] rw [ih₂] simp only [reverse_cons, append_assoc, singleton_append] apply congrArg simp only [unique] rw [ih₃] rw [reverse_singleton, singleton_append, filter_filter] have : (λ x_1 => decide ( (decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) ) = (λ x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) := by apply funext intro x_1 simp only [decide_not, Bool.not_eq_true'] cases Decidable.em (x_1 ∈ acc) with | inl hmem => simp only [hmem, decide_True, not_true_eq_false, false_and] | inr hnmem => simp only [hnmem, decide_False, not_false_eq_true, true_and, decide_not] cases Decidable.em (x_1 ∈ [x]) with | inl hmem' => simp only [hmem', decide_True, decide_False, not] | inr hnmem' => simp only [hnmem', decide_True, decide_False, not] rw [this, ←unique] apply congrArg apply congrArg have h_mem_iff := mem_cons_iff_mem_singleton_or_tail x acc have h_mem_iff_neg := (λ x => Iff.not_iff_not_of_iff $ h_mem_iff x) apply congr _ rfl apply congr rfl apply funext intros a apply Decidable.prop_eq_of_decide_eq rw [h_mem_iff_neg, not_or_distrib, And.comm]
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) ⊢ (if x ∈ acc then uniqueAux xs acc else uniqueAux xs (x :: acc)) = reverse acc ++ unique (match decide ¬x ∈ acc with | true => x :: filter (fun x => decide ¬x ∈ acc) xs | false => filter (fun x => decide ¬x ∈ acc) xs)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [hin, ite_true, not_true_eq_false, decide_False]
case inl α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hin : x ∈ acc ⊢ (if x ∈ acc then uniqueAux xs acc else uniqueAux xs (x :: acc)) = reverse acc ++ unique (match decide ¬x ∈ acc with | true => x :: filter (fun x => decide ¬x ∈ acc) xs | false => filter (fun x => decide ¬x ∈ acc) xs)
case inl α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hin : x ∈ acc ⊢ uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
rw [ih₁]
case inl α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hin : x ∈ acc ⊢ uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs)
no goals
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [hout, ite_false, not_false_eq_true, decide_True]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ (if x ∈ acc then uniqueAux xs acc else uniqueAux xs (x :: acc)) = reverse acc ++ unique (match decide ¬x ∈ acc with | true => x :: filter (fun x => decide ¬x ∈ acc) xs | false => filter (fun x => decide ¬x ∈ acc) xs)
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ uniqueAux xs (x :: acc) = reverse acc ++ unique (x :: filter (fun x => decide ¬x ∈ acc) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [reverse_singleton, singleton_append, unique, uniqueAux, List.not_mem_nil, ite_false]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ uniqueAux xs (x :: acc) = reverse acc ++ unique (x :: filter (fun x => decide ¬x ∈ acc) xs)
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ uniqueAux xs (x :: acc) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
rw [ih₂]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ uniqueAux xs (x :: acc) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [reverse_cons, append_assoc, singleton_append]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ reverse acc ++ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
apply congrArg
case inr α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ reverse acc ++ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = reverse acc ++ uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
simp only [unique]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
rw [ih₃]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = uniqueAux (filter (fun x => decide ¬x ∈ acc) xs) [x]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
rw [reverse_singleton, singleton_append, filter_filter]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs))
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = x :: unique (filter (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
have : (λ x_1 => decide ( (decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true) ) = (λ x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) := by apply funext intro x_1 simp only [decide_not, Bool.not_eq_true'] cases Decidable.em (x_1 ∈ acc) with | inl hmem => simp only [hmem, decide_True, not_true_eq_false, false_and] | inr hnmem => simp only [hnmem, decide_False, not_false_eq_true, true_and, decide_not] cases Decidable.em (x_1 ∈ [x]) with | inl hmem' => simp only [hmem', decide_True, decide_False, not] | inr hnmem' => simp only [hnmem', decide_True, decide_False, not]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = x :: unique (filter (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) xs)
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = x :: unique (filter (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
rw [this, ←unique]
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ x :: uniqueAux (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) [] = x :: unique (filter (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) xs)
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = x :: unique (filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
apply congrArg
case inr.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ x :: unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = x :: unique (filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs)
case inr.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = unique (filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs)
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
apply congrArg
case inr.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) = unique (filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs)
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
have h_mem_iff := mem_cons_iff_mem_singleton_or_tail x acc
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
have h_mem_iff_neg := (λ x => Iff.not_iff_not_of_iff $ h_mem_iff x)
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc) ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
apply congr _ rfl
case inr.h.h.h α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc) ⊢ filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs = filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc) ⊢ (filter fun x_1 => decide ¬x_1 ∈ x :: acc) = fun xs => filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
https://github.com/jrr6/lean-tables.git
7dfa8308e13cb7b15296cc63fa2cbd26c0d0f712
Table/BuiltinExtensions.lean
List.uniqueAux_acc_append_filter
[1075, 1]
[1134, 25]
apply congr rfl
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc) ⊢ (filter fun x_1 => decide ¬x_1 ∈ x :: acc) = fun xs => filter (fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])) xs
α : Type u_1 inst✝ : DecidableEq α x : α xs acc : List α hterm : length (filter (fun a => decide ¬a ∈ acc) xs) < Nat.succ (length xs) hterm' : length xs < Nat.succ (length xs) ih₁ : uniqueAux xs acc = reverse acc ++ unique (filter (fun x => decide ¬x ∈ acc) xs) ih₂ : uniqueAux xs (x :: acc) = reverse (x :: acc) ++ unique (filter (fun x_1 => decide ¬x_1 ∈ x :: acc) xs) ih₃ : uniqueAux (filter (fun a => decide ¬a ∈ acc) xs) [x] = reverse [x] ++ unique (filter (fun x_1 => decide ¬x_1 ∈ [x]) (filter (fun a => decide ¬a ∈ acc) xs)) hout : ¬x ∈ acc this : (fun x_1 => decide ((decide ¬x_1 ∈ acc) = true ∧ (decide ¬x_1 ∈ [x]) = true)) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x]) h_mem_iff : ∀ (x_1 : α), x_1 ∈ x :: acc ↔ x_1 ∈ [x] ∨ x_1 ∈ acc h_mem_iff_neg : ∀ (x_1 : α), ¬x_1 ∈ x :: acc ↔ ¬(x_1 ∈ [x] ∨ x_1 ∈ acc) ⊢ (fun x_1 => decide ¬x_1 ∈ x :: acc) = fun x_1 => decide (¬x_1 ∈ acc ∧ ¬x_1 ∈ [x])