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/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | case nil =>
simp only [Function.updateListITE] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
ys : List β
⊢ g ∘ updateListITE f [] ys = updateListITE (g ∘ f) [] (List.map g ys) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | case cons _ xs_hd xs_tl xs_ih =>
cases ys
case nil =>
simp
simp only [Function.updateListITE]
case cons ys_hd ys_tl =>
simp
simp only [Function.updateListITE]
simp only [← xs_ih]
apply Function.updateITE_comp_left | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) ys = updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g ys) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp only [Function.updateListITE] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
ys : List β
⊢ g ∘ updateListITE f [] ys = updateListITE (g ∘ f) [] (List.map g ys) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | cases ys | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) ys = updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g ys) | case nil
α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) [] = updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g [])
case cons
α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
head✝ : β
tail✝ : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) (head✝ :: tail✝) =
updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g (head✝ :: tail✝)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | case nil =>
simp
simp only [Function.updateListITE] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) [] = updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g []) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | case cons ys_hd ys_tl =>
simp
simp only [Function.updateListITE]
simp only [← xs_ih]
apply Function.updateITE_comp_left | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) =
updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g (ys_hd :: ys_tl)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) [] = updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g []) | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) [] = updateListITE (g ∘ f) (xs_hd :: xs_tl) [] |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp only [Function.updateListITE] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) [] = updateListITE (g ∘ f) (xs_hd :: xs_tl) [] | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) =
updateListITE (g ∘ f) (xs_hd :: xs_tl) (List.map g (ys_hd :: ys_tl)) | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) =
updateListITE (g ∘ f) (xs_hd :: xs_tl) (g ys_hd :: List.map g ys_tl) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp only [Function.updateListITE] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) =
updateListITE (g ∘ f) (xs_hd :: xs_tl) (g ys_hd :: List.map g ys_tl) | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd =
updateITE (updateListITE (g ∘ f) xs_tl (List.map g ys_tl)) xs_hd (g ys_hd) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | simp only [← xs_ih] | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd =
updateITE (updateListITE (g ∘ f) xs_tl (List.map g ys_tl)) xs_hd (g ys_hd) | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd = updateITE (g ∘ updateListITE f xs_tl ys_tl) xs_hd (g ys_hd) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | apply Function.updateITE_comp_left | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), g ∘ updateListITE f xs_tl ys = updateListITE (g ∘ f) xs_tl (List.map g ys)
ys_hd : β
ys_tl : List β
⊢ g ∘ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd = updateITE (g ∘ updateListITE f xs_tl ys_tl) xs_hd (g ys_hd) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | induction xs generalizing ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
xs ys : List α
x : α
h1 : f x = g x
⊢ updateListITE f xs (List.map f ys) x = updateListITE g xs (List.map f ys) x | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ updateListITE f [] (List.map f ys) x = updateListITE g [] (List.map f ys) x
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ (ys : List α), updateListITE f tail✝ (List.map f ys) x = updateListITE g tail✝ (List.map f ys) x
ys : List α
⊢ updateListITE f (head✝ :: tail✝) (List.map f ys) x = updateListITE g (head✝ :: tail✝) (List.map f ys) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | case nil =>
simp only [Function.updateListITE]
exact h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ updateListITE f [] (List.map f ys) x = updateListITE g [] (List.map f ys) x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ updateListITE f [] (List.map f ys) x = updateListITE g [] (List.map f ys) x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ f x = g x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | exact h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ f x = g x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | cases ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys : List α
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f ys) x = updateListITE g (xs_hd :: xs_tl) (List.map f ys) x | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f []) x = updateListITE g (xs_hd :: xs_tl) (List.map f []) x
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
head✝ : α
tail✝ : List α
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f (head✝ :: tail✝)) x =
updateListITE g (xs_hd :: xs_tl) (List.map f (head✝ :: tail✝)) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | case nil =>
simp
simp only [Function.updateListITE]
exact h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f []) x = updateListITE g (xs_hd :: xs_tl) (List.map f []) x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f []) x = updateListITE g (xs_hd :: xs_tl) (List.map f []) x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ updateListITE f (xs_hd :: xs_tl) [] x = updateListITE g (xs_hd :: xs_tl) [] x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ updateListITE f (xs_hd :: xs_tl) [] x = updateListITE g (xs_hd :: xs_tl) [] x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ f x = g x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | exact h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
⊢ f x = g x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ updateListITE f (xs_hd :: xs_tl) (List.map f (ys_hd :: ys_tl)) x =
updateListITE g (xs_hd :: xs_tl) (List.map f (ys_hd :: ys_tl)) x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ updateListITE f (xs_hd :: xs_tl) (f ys_hd :: List.map f ys_tl) x =
updateListITE g (xs_hd :: xs_tl) (f ys_hd :: List.map f ys_tl) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ updateListITE f (xs_hd :: xs_tl) (f ys_hd :: List.map f ys_tl) x =
updateListITE g (xs_hd :: xs_tl) (f ys_hd :: List.map f ys_tl) x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ updateITE (updateListITE f xs_tl (List.map f ys_tl)) xs_hd (f ys_hd) x =
updateITE (updateListITE g xs_tl (List.map f ys_tl)) xs_hd (f ys_hd) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ updateITE (updateListITE f xs_tl (List.map f ys_tl)) xs_hd (f ys_hd) x =
updateITE (updateListITE g xs_tl (List.map f ys_tl)) xs_hd (f ys_hd) x | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ (if x = xs_hd then f ys_hd else updateListITE f xs_tl (List.map f ys_tl) x) =
if x = xs_hd then f ys_hd else updateListITE g xs_tl (List.map f ys_tl) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | split_ifs | α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
⊢ (if x = xs_hd then f ys_hd else updateListITE f xs_tl (List.map f ys_tl) x) =
if x = xs_hd then f ys_hd else updateListITE g xs_tl (List.map f ys_tl) x | case pos
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
h✝ : x = xs_hd
⊢ f ys_hd = f ys_hd
case neg
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
h✝ : ¬x = xs_hd
⊢ updateListITE f xs_tl (List.map f ys_tl) x = updateListITE g xs_tl (List.map f ys_tl) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | rfl | case pos
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
h✝ : x = xs_hd
⊢ f ys_hd = f ys_hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem' | [416, 1] | [442, 26] | exact xs_ih ys_tl | case neg
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List α), updateListITE f xs_tl (List.map f ys) x = updateListITE g xs_tl (List.map f ys) x
ys_hd : α
ys_tl : List α
h✝ : ¬x = xs_hd
⊢ updateListITE f xs_tl (List.map f ys_tl) x = updateListITE g xs_tl (List.map f ys_tl) x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | induction xs generalizing ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
xs : List α
ys : List β
h1 : v ∈ xs
h2 : xs.length = ys.length
⊢ updateListITE f xs ys v = updateListITE g xs ys v | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
ys : List β
h1 : v ∈ []
h2 : [].length = ys.length
⊢ updateListITE f [] ys v = updateListITE g [] ys v
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
v head✝ : α
tail✝ : List α
tail_ih✝ :
∀ (ys : List β), v ∈ tail✝ → tail✝.length = ys.length → updateListITE f tail✝ ys v = updateListITE g tail✝ ys v
ys : List β
h1 : v ∈ head✝ :: tail✝
h2 : (head✝ :: tail✝).length = ys.length
⊢ updateListITE f (head✝ :: tail✝) ys v = updateListITE g (head✝ :: tail✝) ys v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case nil =>
contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
ys : List β
h1 : v ∈ []
h2 : [].length = ys.length
⊢ updateListITE f [] ys v = updateListITE g [] ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case cons xs_hd xs_tl xs_ih =>
simp at h1
cases ys
case nil =>
contradiction
case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
cases h1
case inl h1 =>
simp only [if_pos h1]
case inr h1 =>
split_ifs
case pos =>
rfl
case neg c1 =>
simp at h2
exact xs_ih ys_tl h1 h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h1 : v ∈ xs_hd :: xs_tl
h2 : (xs_hd :: xs_tl).length = ys.length
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
ys : List β
h1 : v ∈ []
h2 : [].length = ys.length
⊢ updateListITE f [] ys v = updateListITE g [] ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | simp at h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h1 : v ∈ xs_hd :: xs_tl
h2 : (xs_hd :: xs_tl).length = ys.length
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h2 : (xs_hd :: xs_tl).length = ys.length
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | cases ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h2 : (xs_hd :: xs_tl).length = ys.length
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
h2 : (xs_hd :: xs_tl).length = [].length
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
head✝ : β
tail✝ : List β
h2 : (xs_hd :: xs_tl).length = (head✝ :: tail✝).length
⊢ updateListITE f (xs_hd :: xs_tl) (head✝ :: tail✝) v = updateListITE g (xs_hd :: xs_tl) (head✝ :: tail✝) v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case nil =>
contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
h2 : (xs_hd :: xs_tl).length = [].length
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
cases h1
case inl h1 =>
simp only [if_pos h1]
case inr h1 =>
split_ifs
case pos =>
rfl
case neg c1 =>
simp at h2
exact xs_ih ys_tl h1 h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
h2 : (xs_hd :: xs_tl).length = [].length
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = updateITE (updateListITE g xs_tl ys_tl) xs_hd ys_hd v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = updateITE (updateListITE g xs_tl ys_tl) xs_hd ys_hd v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | cases h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | case inl
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h✝ : v = xs_hd
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v
case inr
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h✝ : v ∈ xs_tl
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case inl h1 =>
simp only [if_pos h1] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v = xs_hd
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case inr h1 =>
split_ifs
case pos =>
rfl
case neg c1 =>
simp at h2
exact xs_ih ys_tl h1 h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | simp only [if_pos h1] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v = xs_hd
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | split_ifs | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | case pos
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd
case neg
α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
h✝ : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case pos =>
rfl | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | case neg c1 =>
simp at h2
exact xs_ih ys_tl h1 h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | rfl | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | simp at h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h2 : (xs_hd :: xs_tl).length = (ys_hd :: ys_tl).length
h1 : v ∈ xs_tl
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v ∈ xs_tl
c1 : ¬v = xs_hd
h2 : xs_tl.length = ys_tl.length
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem_eq_len | [445, 1] | [478, 34] | exact xs_ih ys_tl h1 h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → xs_tl.length = ys.length → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v ∈ xs_tl
c1 : ¬v = xs_hd
h2 : xs_tl.length = ys_tl.length
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | induction xs generalizing ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
xs : List α
ys : List β
h1 : v ∈ xs
h2 : f v = g v
⊢ updateListITE f xs ys v = updateListITE g xs ys v | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
ys : List β
h1 : v ∈ []
⊢ updateListITE f [] ys v = updateListITE g [] ys v
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ (ys : List β), v ∈ tail✝ → updateListITE f tail✝ ys v = updateListITE g tail✝ ys v
ys : List β
h1 : v ∈ head✝ :: tail✝
⊢ updateListITE f (head✝ :: tail✝) ys v = updateListITE g (head✝ :: tail✝) ys v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case nil =>
contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
ys : List β
h1 : v ∈ []
⊢ updateListITE f [] ys v = updateListITE g [] ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case cons xs_hd xs_tl xs_ih =>
cases ys
case nil =>
simp at h1
simp only [Function.updateListITE]
exact h2
case cons ys_hd ys_tl =>
simp at h1
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos =>
rfl
case neg c1 =>
cases h1
case inl c2 =>
contradiction
case inr c2 =>
exact xs_ih ys_tl c2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
ys : List β
h1 : v ∈ []
⊢ updateListITE f [] ys v = updateListITE g [] ys v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | cases ys | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys : List β
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = updateListITE g (xs_hd :: xs_tl) ys v | case nil
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v
case cons
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
head✝ : β
tail✝ : List β
⊢ updateListITE f (xs_hd :: xs_tl) (head✝ :: tail✝) v = updateListITE g (xs_hd :: xs_tl) (head✝ :: tail✝) v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case nil =>
simp at h1
simp only [Function.updateListITE]
exact h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case cons ys_hd ys_tl =>
simp at h1
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos =>
rfl
case neg c1 =>
cases h1
case inl c2 =>
contradiction
case inr c2 =>
exact xs_ih ys_tl c2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | simp at h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = updateListITE g (xs_hd :: xs_tl) [] v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ f v = g v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | exact h2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ f v = g v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | simp at h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
h1 : v ∈ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = updateListITE g (xs_hd :: xs_tl) (ys_hd :: ys_tl) v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = updateITE (updateListITE g xs_tl ys_tl) xs_hd ys_hd v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = updateITE (updateListITE g xs_tl ys_tl) xs_hd ys_hd v | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | split_ifs | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) =
if v = xs_hd then ys_hd else updateListITE g xs_tl ys_tl v | case pos
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd
case neg
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
h✝ : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case pos =>
rfl | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case neg c1 =>
cases h1
case inl c2 =>
contradiction
case inr c2 =>
exact xs_ih ys_tl c2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | rfl | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
h✝ : v = xs_hd
⊢ ys_hd = ys_hd | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | cases h1 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
h1 : v = xs_hd ∨ v ∈ xs_tl
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | case inl
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h✝ : v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v
case inr
α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h✝ : v ∈ xs_tl
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case inl c2 =>
contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
c2 : v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | case inr c2 =>
exact xs_ih ys_tl c2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
c2 : v ∈ xs_tl
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | contradiction | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
c2 : v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_mem | [481, 1] | [516, 31] | exact xs_ih ys_tl c2 | α β : Type
inst✝ : DecidableEq α
f g : α → β
v : α
h2 : f v = g v
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∈ xs_tl → updateListITE f xs_tl ys v = updateListITE g xs_tl ys v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
c2 : v ∈ xs_tl
⊢ updateListITE f xs_tl ys_tl v = updateListITE g xs_tl ys_tl v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | induction xs generalizing ys | α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
xs : List α
ys : List β
h1 : v ∉ xs
⊢ updateListITE f xs ys v = f v | case nil
α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
ys : List β
h1 : v ∉ []
⊢ updateListITE f [] ys v = f v
case cons
α β : Type
inst✝ : DecidableEq α
f : α → β
v head✝ : α
tail✝ : List α
tail_ih✝ : ∀ (ys : List β), v ∉ tail✝ → updateListITE f tail✝ ys v = f v
ys : List β
h1 : v ∉ head✝ :: tail✝
⊢ updateListITE f (head✝ :: tail✝) ys v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case nil =>
simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
ys : List β
h1 : v ∉ []
⊢ updateListITE f [] ys v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case cons xs_hd xs_tl xs_ih =>
cases ys
case nil =>
simp only [Function.updateListITE]
case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos c1 =>
subst c1
simp at h1
case neg c1 =>
simp at h1
push_neg at h1
cases h1
case intro h1_left h1_right =>
apply xs_ih ys_tl h1_right | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys : List β
h1 : v ∉ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
ys : List β
h1 : v ∉ []
⊢ updateListITE f [] ys v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | cases ys | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys : List β
h1 : v ∉ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) ys v = f v | case nil
α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = f v
case cons
α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
head✝ : β
tail✝ : List β
⊢ updateListITE f (xs_hd :: xs_tl) (head✝ :: tail✝) v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case nil =>
simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos c1 =>
subst c1
simp at h1
case neg c1 =>
simp at h1
push_neg at h1
cases h1
case intro h1_left h1_right =>
apply xs_ih ys_tl h1_right | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
⊢ updateListITE f (xs_hd :: xs_tl) [] v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) v = f v | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ updateITE (updateListITE f xs_tl ys_tl) xs_hd ys_hd v = f v | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | split_ifs | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
⊢ (if v = xs_hd then ys_hd else updateListITE f xs_tl ys_tl v) = f v | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
h✝ : v = xs_hd
⊢ ys_hd = f v
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
h✝ : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case pos c1 =>
subst c1
simp at h1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
c1 : v = xs_hd
⊢ ys_hd = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case neg c1 =>
simp at h1
push_neg at h1
cases h1
case intro h1_left h1_right =>
apply xs_ih ys_tl h1_right | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | subst c1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
c1 : v = xs_hd
⊢ ys_hd = f v | α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
h1 : v ∉ v :: xs_tl
⊢ ys_hd = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp at h1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
h1 : v ∉ v :: xs_tl
⊢ ys_hd = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | simp at h1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
h1 : v ∉ xs_hd :: xs_tl
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
⊢ updateListITE f xs_tl ys_tl v = f v | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1 : ¬v = xs_hd ∧ v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | push_neg at h1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1 : ¬v = xs_hd ∧ v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1 : v ≠ xs_hd ∧ v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | cases h1 | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1 : v ≠ xs_hd ∧ v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v | case intro
α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
left✝ : v ≠ xs_hd
right✝ : v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | case intro h1_left h1_right =>
apply xs_ih ys_tl h1_right | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1_left : v ≠ xs_hd
h1_right : v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_not_mem | [519, 1] | [548, 37] | apply xs_ih ys_tl h1_right | α β : Type
inst✝ : DecidableEq α
f : α → β
v xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), v ∉ xs_tl → updateListITE f xs_tl ys v = f v
ys_hd : β
ys_tl : List β
c1 : ¬v = xs_hd
h1_left : v ≠ xs_hd
h1_right : v ∉ xs_tl
⊢ updateListITE f xs_tl ys_tl v = f v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | induction xs generalizing ys | α β : Type
inst✝ : DecidableEq α
f : α → β
xs : List α
ys : List β
x y : α
z : β
h1 : ¬x = y
⊢ updateListITE (updateITE f y z) xs ys x = updateListITE f xs ys x | case nil
α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ updateListITE (updateITE f y z) [] ys x = updateListITE f [] ys x
case cons
α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ (ys : List β), updateListITE (updateITE f y z) tail✝ ys x = updateListITE f tail✝ ys x
ys : List β
⊢ updateListITE (updateITE f y z) (head✝ :: tail✝) ys x = updateListITE f (head✝ :: tail✝) ys x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | case nil =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
simp only [if_neg h1] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ updateListITE (updateITE f y z) [] ys x = updateListITE f [] ys x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | case cons xs_hd xs_tl xs_ih =>
cases ys
case nil =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
simp only [if_neg h1]
case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos c1 =>
rfl
case neg c1 =>
apply xs_ih | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
ys : List β
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) ys x = updateListITE f (xs_hd :: xs_tl) ys x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ updateListITE (updateITE f y z) [] ys x = updateListITE f [] ys x | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ updateITE f y z x = f x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ updateITE f y z x = f x | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ (if x = y then z else f x) = f x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | simp only [if_neg h1] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
ys : List β
⊢ (if x = y then z else f x) = f x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | cases ys | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
ys : List β
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) ys x = updateListITE f (xs_hd :: xs_tl) ys x | case nil
α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) [] x = updateListITE f (xs_hd :: xs_tl) [] x
case cons
α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
head✝ : β
tail✝ : List β
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) (head✝ :: tail✝) x =
updateListITE f (xs_hd :: xs_tl) (head✝ :: tail✝) x |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | case nil =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
simp only [if_neg h1] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) [] x = updateListITE f (xs_hd :: xs_tl) [] x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | case cons ys_hd ys_tl =>
simp only [Function.updateListITE]
simp only [Function.updateITE]
split_ifs
case pos c1 =>
rfl
case neg c1 =>
apply xs_ih | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
ys_hd : β
ys_tl : List β
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) (ys_hd :: ys_tl) x =
updateListITE f (xs_hd :: xs_tl) (ys_hd :: ys_tl) x | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_updateIte | [551, 1] | [581, 20] | simp only [Function.updateListITE] | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
⊢ updateListITE (updateITE f y z) (xs_hd :: xs_tl) [] x = updateListITE f (xs_hd :: xs_tl) [] x | α β : Type
inst✝ : DecidableEq α
f : α → β
x y : α
z : β
h1 : ¬x = y
xs_hd : α
xs_tl : List α
xs_ih : ∀ (ys : List β), updateListITE (updateITE f y z) xs_tl ys x = updateListITE f xs_tl ys x
⊢ updateITE f y z x = f x |
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