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 | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | funext x | α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
⊢ updateITE (updateITE f a c) b d = updateITE (updateITE f b d) a c | case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ updateITE (updateITE f a c) b d x = updateITE (updateITE f b d) a c x | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
⊢ updateITE (updateITE f a c) b d = updateITE (updateITE f b d) a c
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | simp only [Function.updateITE] | case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ updateITE (updateITE f a c) b d x = updateITE (updateITE f b d) a c x | case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ updateITE (updateITE f a c) b d x = updateITE (updateITE f b d) a c x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | by_cases c1 : x = a | case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
⊢ (if x = b then d else if... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | by_cases c2 : x = b | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : ¬x = b
⊢ (i... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | subst c1 | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 : x = b
h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | subst c2 | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 : x = b
h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
c d : β
x : α
h1 : ¬x = x
⊢ (if x = x then d else if x = x then c else f x) = if x = x then c else if x = x then d else f x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 : x = b
h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | contradiction | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
c d : β
x : α
h1 : ¬x = x
⊢ (if x = x then d else if x = x then c else f x) = if x = x then c else if x = x then d else f x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
c d : β
x : α
h1 : ¬x = x
⊢ (if x = x then d else if x = x then c else f x) = if x = x then c else if x = x then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | subst c1 | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : ¬x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : x = a
c2 : ¬x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | simp | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ x = b → d = c | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ (if x = b then d else if x = x then c else f x) = if x = x then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | intro a1 | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ x = b → d = c | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
a1 : x = b
⊢ d = c | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
⊢ x = b → d = c
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | contradiction | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
a1 : x = b
⊢ d = c | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
b : α
c d : β
x : α
c2 h1 : ¬x = b
a1 : x = b
⊢ d = c
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | by_cases c2 : x = b | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : ¬x = b
⊢ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | subst c2 | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ (if x = x then d else if x = a then c else f x) = if x = a then c else if x = x then d else f x | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | simp | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ (if x = x then d else if x = a then c else f x) = if x = a then c else if x = x then d else f x | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ d = if x = a then c else d | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ (if x = x then d else if x = a then c else f x) = if x = a then c else if x = x then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | simp only [if_neg c1] | case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ d = if x = a then c else d | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
f : α → β
a : α
c d : β
x : α
c1 : ¬x = a
h1 : ¬a = x
⊢ d = if x = a then c else d
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_symm | [342, 1] | [367, 28] | simp only [if_neg c1] | case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : ¬x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
f : α → β
a b : α
c d : β
h1 : ¬a = b
x : α
c1 : ¬x = a
c2 : ¬x = b
⊢ (if x = b then d else if x = a then c else f x) = if x = a then c else if x = b then d else f x
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | simp only [Function.updateITE] | α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
⊢ updateITE g c d (updateITE f b c a) = updateITE (g ∘ f) b d a | α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
⊢ updateITE g c d (updateITE f b c a) = updateITE (g ∘ f) b d a
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | by_cases c1 : a = b | α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a | case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a
case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c ... | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | simp only [c1] | case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a | case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if True then c else f b) = c then d else g (if True then c else f b)) = if True then d else (g ∘ f) b | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | simp | case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if True then c else f b) = c then d else g (if True then c else f b)) = if True then d else (g ∘ f) b | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : a = b
⊢ (if (if True then c else f b) = c then d else g (if True then c else f b)) = if True then d else (g ∘ f) b
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | simp only [c1] | case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a | case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ (if (if False then c else f a) = c then d else g (if False then c else f a)) = if False then d else (g ∘ f) a | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ (if (if a = b then c else f a) = c then d else g (if a = b then c else f a)) = if a = b then d else (g ∘ f) a
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | simp | case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ (if (if False then c else f a) = c then d else g (if False then c else f a)) = if False then d else (g ∘ f) a | case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ f a = c → d = g (f a) | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ (if (if False then c else f a) = c then d else g (if False then c else f a)) = if False then d else (g ∘ f) a
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateITE_comp | [370, 1] | [386, 13] | exact h1 | case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ f a = c → d = g (f a) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
α β : Type
inst✝ : DecidableEq α
a b c : α
d : β
f : α → α
g : α → β
h1 : f a = c → d = g (f a)
c1 : ¬a = b
⊢ f a = c → d = g (f a)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/FunctionUpdateITE.lean | Function.updateListITE_comp | [391, 1] | [413, 41] | induction xs generalizing ys | α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs : List α
ys : List β
⊢ g ∘ updateListITE f xs ys = updateListITE (g ∘ f) xs (List.map g ys) | case nil
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)
case cons
α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
head✝ : α
tail✝ : List α
tail_ih✝ : ∀ (ys : List β), g ∘ updateListITE f tail✝ ys = updateListITE (g ∘ f) t... | Please generate a tactic in lean4 to solve the state.
STATE:
α β γ : Type
inst✝ : DecidableEq α
f : α → β
g : β → γ
xs : List α
ys : List β
⊢ g ∘ updateListITE f xs ys = updateListITE (g ∘ f) xs (List.map g ys)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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) (... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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✝ : ... | Please generate a tactic in lean4 to solve the state.
STATE:
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) (... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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 (y... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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) [] | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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 (y... | 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 :: Li... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 :: Li... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 ... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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✝ (Li... | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
f g : α → β
x : α
h1 : f x = g x
ys : List α
⊢ f x = g x
TACTIC:
|
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 c... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = update... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = update... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 :... | 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 :... | Please generate a tactic in lean4 to solve the state.
STATE:
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) (... |
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 :... | 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 (updateL... | Please generate a tactic in lean4 to solve the state.
STATE:
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) (... |
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 (updateL... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 (... |
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 ... | 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 → ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 up... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = ... |
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 (Li... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ updateLis... |
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 → updat... | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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
c... | 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 = updateLis... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 = ... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 = updateLis... | 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 = update... | Please generate a tactic in lean4 to solve the state.
STATE:
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 = ... |
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 = update... | 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 = updateLis... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 (x... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: ... |
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 (x... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | 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 (updateLi... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: ... |
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 (updateLi... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: ... |
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 ... | 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_... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: ... |
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 u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 u... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 u... | 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 =... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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... | 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 = updat... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :: y... |
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 = updat... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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.... |
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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
c... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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
i... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = updateLis... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 :... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = updateLis... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 = update... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 :... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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_h... |
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... | 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 th... | Please generate a tactic in lean4 to solve the state.
STATE:
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 (updateList... |
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 th... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ updat... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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 i... | Please generate a tactic in lean4 to solve the state.
STATE:
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
⊢ updat... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 x... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 x... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 x... |
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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 x... |
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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
ys : List β
h1 : v ∉ []
⊢ updateListITE f [] ys v = f v
TACTIC:
|
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
... | 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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
α β : Type
inst✝ : DecidableEq α
f : α → β
v : α
ys : List β
h1 : v ∉ []
⊢ updateListITE f [] ys v = f v
TACTIC:
|
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... | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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