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/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case a.h.e'_4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | case a.h.e'_4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c1 : x β binders' | case a.h.e'_4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName)... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h2 x c1 | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignmen... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply h3 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName)... | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignmen... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact ih_1 x a1 c1 | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNam... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : PredName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignm... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | congr! 1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v... | case a.h.e'_2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c1 : x β binders' | case a.h.e'_2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h2 x c1 | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssign... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply h3 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssign... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply ih_1 | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact c1 | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c1 : y β binders' | case a.h.e'_3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h2 y c1 | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssign... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply h3 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarNa... | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssign... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply ih_1 | case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : Var... | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact c1 | case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : V... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.a.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x y : VarName
ih_1 : β (v : VarName), v = x β¨ v = y β v β binders' β Ο' v β binders'
V V' : VarAs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Οβ : VarName β VarName
bindersβ : Finset VarName
V V' : VarAssignment D
h2 : β v β bindersβ, V v = V' (Οβ v)
h3 : β (v : VarName), Οβ v β bindersβ β V v = V' (Οβ v)
h4 : β v β bindersβ, v = Οβ v
β’ Holds D I V E false_ β ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Οβ : VarName β VarName
bindersβ : Finset VarName
V V' : VarAssignment D
h2 : β v β bindersβ, V v = V' (Οβ v)
h3 : β (v : VarName), Οβ v β bindersβ β V v = V' (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (Ο' v)) β
(β (v : VarName), Ο' v β binders' ... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (Ο' v)) β
(β (v : VarName), Ο' v β binders' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | congr! 1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (Ο' v)) β
(β (v : VarName), Ο' v β binders' ... | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (Ο' v)) β
(β (v : VarName), ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact ih_2 V V' h2 h3 h4 | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (Ο' v)) β
(β (v : VarName), ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi phi' : Formula
aβ : IsSubAux Ο' binders' phi phi'
ih_2 :
β (V V' : VarAssignment D),
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | congr! 1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β binders', V v = V' (... | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β bind... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply phi_ih_2 V V' h2 h3 h4 | case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β bind... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply psi_ih_2 V V' h2 h3 h4 | case a.h.e'_2.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi psi'
phi_ih_2 :
β (V V' : VarAssignment D),
(β v β bind... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
phi psi phi' psi' : Formula
aβΒΉ : IsSubAux Ο' binders' phi phi'
aβ : IsSubAux Ο' binders' psi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp at ih_2 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
ih_2 :
β (V V' : VarAssignment D),
(β v β binders' βͺ {x}, V v = V'... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
ih_2 :
β ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | have s1 : β (v : VarName), Β¬ v = x β v β binders' β Β¬ Ο' v = x | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro v a1 a2 contra | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply a1 | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [β contra] | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h4 v a2 | case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 :... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | first | apply forall_congr'| apply exists_congr | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro d | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply ih_2 | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply forall_congr' | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply exists_congr | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case h
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro v a1 | case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c1 : v = x | case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h2
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_pos c1] | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_neg c1] | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | cases a1 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg.inl
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c2 =>
simp only [s1 v c1 c2]
simp
exact h2 v c2 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c2 =>
contradiction | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [s1 v c1 c2] | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h2 v c2 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | contradiction | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro v a1 | case h.h3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case h.h3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c1 : v = x | case h.h3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h3
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_pos c1] | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] at a1 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_neg c1] at a1 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_neg c1] | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro a2 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [if_neg a2] | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply h3 v a1 | case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro v a1 | case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Function.updateITE] | case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | split_ifs | case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3... | case pos
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h.h4
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c1 =>
exact c1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c1 =>
cases a1
case _ c2 =>
exact h4 v c2
case _ c2 =>
contradiction | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact c1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | cases a1 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | case inl
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c2 =>
exact h4 v c2 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c2 =>
contradiction | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact h4 v c2 | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | contradiction | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
x : VarName
phi phi' : Formula
aβ : IsSubAux (Function.updateITE Ο' x x) (binders' βͺ {x}) phi phi'
V V' : VarA... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | induction E | D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case nil
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case nil =>
simp only [Holds] | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [Holds] | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | split_ifs | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | case pos
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c1 c2 =>
simp only [List.length_map] at c2
contradiction | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c1 c2 =>
simp at c2
contradiction | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | case _ c1 c2 =>
exact ih | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply Holds_coincide_Var | D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β binders' ... | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β bin... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro v a1 | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | have s1 : List.map V xs' = List.map (V' β Ο') xs' | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [List.map_eq_map_iff] | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | intro x a2 | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | by_cases c3 : x β binders' | case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case pos
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [s1] | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | apply Function.updateListITE_mem_eq_len | case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v β b... | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp only [isFreeIn_iff_mem_freeVarSet] at a1 | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | obtain s2 := hd.h1 a1 | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp at s2 | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | exact s2 | case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp at c2 | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | simp | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Var/All/Ind/Sub.lean | FOL.NV.Sub.Var.All.Ind.substitution_theorem_aux | [129, 1] | [273, 17] | tauto | case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 : β v β binders', V v = V' (Ο' v)
h3 : β (v : VarName), Ο' v ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
D : Type
I : Interpretation D
Ο : VarName β VarName
binders : Finset VarName
F F' : Formula
Ο' : VarName β VarName
binders' : Finset VarName
X' : DefName
xs' : List VarName
ih_1 : β v β xs', v β binders' β Ο' v β binders'
V V' : VarAssignment D
h2 ... |
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