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/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case _ c2 =>
subst c1
simp only [Function.updateITE_idem] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case _ c2 =>
subst c1
simp only [Function.updateITE_idem] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | subst c1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Function.updateITE_idem] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuatio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | subst c1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Function.updateITE_idem] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
V : Valuation D
d d' : D
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
phi_ih :
NotFree Ξ x phi β β (V : Valuatio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | cases h1 | case neg
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE... | case neg.inl
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D)... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case _ c2 =>
contradiction | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case _ c2 =>
simp only [β Function.updateITE_comm V x v d d' c1]
exact phi_ih c2 (Function.updateITE V x d') d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | contradiction | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [β Function.updateITE_comm V x v d d' c1] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact phi_ih c2 (Function.updateITE V x d') d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | induction E | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
β’ IsNotFree D I M E (def_ X xs) v | case nil
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ IsNotFree D I M [] (def_ X xs) v
case cons
D : Type
I : Interpretation D
M : Met... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
β’ IsNotFree D I M E (def... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case nil =>
unfold IsNotFree
intro V d
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ IsNotFree D I M [] (def_ X xs) v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ IsNotFree D I M [] (def_ X xs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ IsNotFree D I M [] (def_ X xs) v | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ β (V : Valuation D) (d : D), Holds D I V M [] (def_ X xs) β Holds D I (Function.updateITE ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ IsNotFree D I M [] (def_ X xs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ β (V : Valuation D) (d : D), Holds D I V M [] (def_ X xs) β Holds D I (Function.updateITE ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
V : Valuation D
d : D
β’ Holds D I V M [] (def_ X xs) β Holds D I (Function.updateITE V v d) ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
β’ β (V : Valuation D) (d : D), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
V : Valuation D
d : D
β’ Holds D I V M [] (def_ X xs) β Holds D I (Function.updateITE V v d) ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M [] (meta_var_ X) v
V : Valuation D
d : D
β’ Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h2 : β (... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h2 : β (X : MetaVarName), (v, X) β Ξ ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
h1 : NotFree Ξ v (def_ X xs)
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at h2 | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h2 : β (X : MetaVarName), (v, X) β Ξ ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h2 :
β (X : MetaVarName),
(v, X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] at h2 | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h2 :
β (X : MetaVarName),
(v, X... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h1 : v β xs
h2 : β (X : MetaVarName),... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at E_ih | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D I M E_tl (def_ X xs) v
h1 : v β xs
h2 : β (X : MetaVarName),... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih :
(β (X : MetaVarName),
(v, X) β Ξ β
β (V : Valuation D) (d : D),
Holds D I V M E_tl (meta_var_ X) β Holds D I (Function.up... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih : (β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E_tl (meta_var_ X) v) β IsNotFree D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] at E_ih | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih :
(β (X : MetaVarName),
(v, X) β Ξ β
β (V : Valuation D) (d : D),
Holds D I V M E_tl (meta_var_ X) β Holds D I (Function.up... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
E_ih :
(β (X : MetaVarName),
(v, X) β Ξ β
β (V : Valuation D) (d : D),
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V a | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | split_ifs | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | case pos
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case _ c1 =>
exact E_ih h2 V a | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | apply holds_coincide_var D I (Function.updateListITE V E_hd.args (List.map V xs)) (Function.updateListITE (Function.updateITE V v a) E_hd.args (List.map (Function.updateITE V v a) xs)) M E_tl E_hd.F E_hd.args E_hd.nf | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro v' a1 | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | apply Function.updateListITE_map_updateIte V (Function.updateITE V v a) | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro y a2 contra | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | subst contra | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
V : Valuation D
a : D
c1 : X = E_hd.name β§ xs.length = E_hd.args.length
v' : VarName
a1 : v' β E_hd.args
y : VarName
a2 : y β xs
h1 : y β xs
h2 : β (X : MetaV... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | contradiction | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
V : Valuation D
a : D
c1 : X = E_hd.name β§ xs.length = E_hd.args.length
v' : VarName
a1 : v' β E_hd.args
y : VarName
a2 : y β xs
h1 : y β xs
h2 : β (X : MetaV... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
V : Valuation D
a : D
c1 : X = E_hd.name β§ xs.length = E_hd.args.length
v' : VarName
a1 : v' β E_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | cases c1 | case h2
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | case h2.intro
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : Meta... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case intro c1_left c1_right =>
simp only [c1_right] | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [c1_right] | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact a1 | case h3
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarNam... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact E_ih h2 V a | D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (Function.updateITE V v d)
E_ih :
(β (X : MetaVarName), (v, ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ξ : List (VarName Γ MetaVarName)
v : VarName
X : DefName
xs : List VarName
E_hd : Definition
E_tl : List Definition
h1 : v β xs
h2 : β (X : MetaVarName), (v, X) β Ξ β β (V : Valuation D) (d : D), M X V β M X (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | intro v X a1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | cases h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h1 : βΟ β Ο' = id β§ Ο' β βΟ = id
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | simp only [Function.updateITE_comp_right Ο' Ο.1 V v d h1_left h1_right] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ v) (Ο X... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ v) (Ο X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | apply not_free_imp_is_not_free D I M E (Ο X) Ξ' (Ο.1 v) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ v) (Ο X... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | exact h3 v X a1 | case h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | intro X' a2 | case h2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ... | case h2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_1 | [1737, 1] | [1763, 29] | exact h2 (Ο.1 v) X' a2 | case h2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β NotFree Ξ' (βΟ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ Ξ' : List (VarName Γ MetaVarName)
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : β (v : VarName) (X : MetaVarName), (v, X) β Ξ' β IsNotFree D I M E (meta_var_ X) v
h3 : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | induction F | E : Env
Ο : Instantiation
Ο : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E F
h2 : β X β F.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο F) | case meta_var_
E : Env
Ο : Instantiation
Ο : MetaInstantiation
aβ : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ aβ)
h2 : β X β (meta_var_ aβ).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ aβ))
case pred_
E : Env
Ο : Instantiation
Ο : MetaInstantiation
aβΒΉ : PredName... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E F
h2 : β X β F.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case meta_var_ X =>
unfold Formula.metaVarSet at h2
simp at h2
unfold sub
exact h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β (meta_var_ X).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β (meta_var_ X).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case pred_ X xs =>
unfold sub
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (pred_ X xs)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (pred_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case eq_ x y =>
unfold sub
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (eq_ x y)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case true_ =>
unfold sub
unfold IsMetaVarOrAllDefInEnv
simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο true_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case not_ phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h1
unfold Formula.metaVarSet at h2
unfold sub
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h1 h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
h2 : β X β phi.not_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrA... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
h2 : β X β phi.n... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case forall_ x phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h1
unfold Formula.metaVarSet at h2
unfold sub
unfold IsMetaVarOrAllDefInEnv
exact phi_ih h1 h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
h2 : β X β (forall_ x phi).metaVarSet, IsMetaVarOrAllDefIn... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x ph... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | case def_ X xs =>
unfold IsMetaVarOrAllDefInEnv at h1
unfold sub
unfold IsMetaVarOrAllDefInEnv
simp
exact h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold Formula.metaVarSet at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β (meta_var_ X).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β {X}, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β (meta_var_ X).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β {X}, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : β X_1 β {X}, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (Ο X) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (meta_var_ X))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | exact h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (Ο X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : MetaVarName
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2 : IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (Ο X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (pred_ X xs)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (βΟ) xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (pred_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (βΟ) xs)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (pred_ X (List.map (βΟ) xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : PredName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
h2 : β X_1 β (pred_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (eq_ x y)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (eq_ (βΟ x) (βΟ y)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (eq_ (βΟ x) (βΟ y)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (eq_ (βΟ x) (βΟ y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x y : VarName
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
h2 : β X β (eq_ x y).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο true_) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E true_ | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E true_ | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv E true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp only | E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
h1 : IsMetaVarOrAllDefInEnv E true_
h2 : β X β true_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
h2 : β X β phi.not_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrA... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β phi.not_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDef... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi.not_
h2 : β X β phi.n... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold Formula.metaVarSet at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β phi.not_.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
h1 : IsMetaVarOrAllDefInEnv E phi
β’ IsMetaVarOrAllDef... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β phi.not_.metaVarSet, IsMetaVarOrAllDefInEnv ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | exact phi_ih h1 h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarOrAllDefInEnv... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold Formula.metaVarSet at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | cases h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | case intro
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | constructor | E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVar... | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | apply phi_ih h1_left | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | intro X a1 | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | apply h2 | case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β... | case left.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X))... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | left | case left.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X))... | case left.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X... | Please generate a tactic in lean4 to solve the state.
STATE:
case left.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | exact a1 | case left.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | apply psi_ih h1_right | case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | intro X a1 | case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | apply h2 | case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) ... | case right.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)... | Please generate a tactic in lean4 to solve the state.
STATE:
case right
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | right | case right.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)... | case right.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο ... | Please generate a tactic in lean4 to solve the state.
STATE:
case right.a
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E ps... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | exact a1 | case right.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E psi β
(β X β psi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right.a.h
E : Env
Ο : Instantiation
Ο : MetaInstantiation
phi psi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
psi_ih :
IsMetaVarOrAllDefInEnv E ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
h2 : β X β (forall_ x phi).metaVarSet, IsMetaVarOrAllDefIn... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β (forall_ x phi).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
h1 : IsMetaVarOrAllDefInEnv E phi
... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E (forall_ x ph... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold Formula.metaVarSet at h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β (forall_ x phi).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
h1 : IsMetaVarOrAllDefInEnv E phi
... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h2 : β X β (forall_ x phi).metaVarSet, IsMe... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | exact phi_ih h1 h2 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)
β’ IsMetaVarO... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
IsMetaVarOrAllDefInEnv E phi β
(β X β phi.metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X)) β IsMetaVarOrAllDefInEnv E (sub Ο Ο phi)
h1 : IsMetaVarOrAllDefInEnv E phi
h2 : β X ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv at h1 | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold sub | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (sub Ο Ο (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | unfold IsMetaVarOrAllDefInEnv | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs)) | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args.length | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ IsMetaVarOrAllDefInEnv E (def_ X (List.map (βΟ) xs))
TAC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_2_a | [1766, 1] | [1837, 13] | simp | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args.length | E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ xs.length = d.args.length | Please generate a tactic in lean4 to solve the state.
STATE:
E : Env
Ο : Instantiation
Ο : MetaInstantiation
X : DefName
xs : List VarName
h2 : β X_1 β (def_ X xs).metaVarSet, IsMetaVarOrAllDefInEnv E (Ο X_1)
h1 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β d β E, X = d.name β§ (List.map (βΟ) xs).length = d.args... |
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