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.holds_is_proof | [2060, 1] | [2162, 13] | exact a2 d | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | have s1 : IsNotFree D I M E h1_phi h1_x | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply not_free_imp_is_not_free D I M E h1_phi h1_Ξ h1_x h1_2 | case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : Var... | case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : Var... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact nf h1_x | case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : Var... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | unfold IsNotFree at s1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [β s1 V a] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact a1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | unfold exists_ | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply Exists.intro (V h1_y) | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | unfold Function.updateITE | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | trans V h1_x | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [a1] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y h1_z : VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | sorry | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_n : β
h1_name : PredName
h1_xs h1_ys : Fin h1_n β VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_n : β
h1_name : PredName
h1_xs h1_ys : Fin h1_n β VarName
M : MetaValuation D
nf :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | obtain β¨Ο', a1β© := h1_Ο.2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο X)
h1_2 ... | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | have s1 : IsMetaVarOrAllDefInEnv E h1_phi := is_proof_imp_is_meta_var_or_all_def_in_env E h1_Ξ h1_Ξ h1_phi h1_4 | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [β holds_sub D I V M E h1_Ο Ο' h1_Ο h1_phi s1 a1] | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply h1_ih_2 | case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro v X a2 | case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E ... | case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact lem_1 D I M E h1_Ξ h1_Ξ' h1_Ο Ο' h1_Ο a1 nf h1_2 v X a2 | case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.nf
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiat... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro psi V' a2 | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | have s2 : IsMetaVarOrAllDefInEnv E psi | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case s2
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply lem_2_b E h1_Ο h1_Ο | case s2
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply is_proof_imp_is_meta_var_or_all_def_in_env E h1_Ξ' h1_Ξ' (sub h1_Ο h1_Ο psi) | case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact h1_3 psi a2 | case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2.h1
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | have s3 : β V'' : Valuation D, Holds D I (V'' β h1_Ο.val) (fun (X' : MetaVarName) (V' : Valuation D) => Holds D I (V' β Ο') M E (h1_Ο X')) E psi | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V'' | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [holds_sub D I V'' M E h1_Ο Ο' h1_Ο psi s2 a1] | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact h1_ih_1 psi a2 M nf hyp V'' | case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E (h1_Ο ... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case s3
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | specialize s3 (V' β Ο') | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Function.comp.assoc] at s3 | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [a1.right] at s3 | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Function.comp_id] at s3 | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact s3 | case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantiation
h1_1 : β X β h1_phi.metaVarSet, IsMetaVarOrAllDefInEnv E... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro.hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ h1_Ξ' : List (VarName Γ MetaVarName)
h1_Ξ h1_Ξ' : List Formula
h1_phi : Formula
h1_Ο : Instantiation
h1_Ο : MetaInstantia... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | have s1 : Holds D I V M E h1_phi := h1_ih M nf hyp V | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [β holds_conv D I V M E h1_phi h1_phi' h2 h1_3] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact s1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | induction F generalizing vs | F : Formula
vs : List VarName
v : VarName
Ξ : List (VarName Γ MetaVarName)
h1 : NoMetaVarAndAllFreeInList vs F
h2 : v β vs
β’ NotFree Ξ v F | case meta_var_
v : VarName
Ξ : List (VarName Γ MetaVarName)
aβ : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ aβ)
h2 : v β vs
β’ NotFree Ξ v (meta_var_ aβ)
case pred_
v : VarName
Ξ : List (VarName Γ MetaVarName)
aβΒΉ : PredName
aβ vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ a... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
vs : List VarName
v : VarName
Ξ : List (VarName Γ MetaVarName)
h1 : NoMetaVarAndAllFreeInList vs F
h2 : v β vs
β’ NotFree Ξ v F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | case meta_var_ X =>
unfold NoMetaVarAndAllFreeInList at h1
contradiction | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
h2 : v β vs
β’ NotFree Ξ v (meta_var_ X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
h2 : v β vs
β’ NotFree Ξ v (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | case pred_ X xs =>
unfold NoMetaVarAndAllFreeInList at h1
unfold NotFree
tauto | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
h2 : v β vs
β’ NotFree Ξ v (pred_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
h2 : v β vs
β’ NotFree Ξ v (pred_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | case true_ =>
unfold NotFree
simp | v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ NotFree Ξ v true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ NotFree Ξ v true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | case not_ phi phi_ih =>
unfold NoMetaVarAndAllFreeInList at h1
unfold NotFree
exact phi_ih vs h1 h2 | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
h2 : v β vs
β’ NotFree Ξ v phi.not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
h2 : v β vs
β’ NotFree Ξ v phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | case def_ X xs =>
unfold NoMetaVarAndAllFreeInList at h1
unfold NotFree
tauto | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
h2 : v β vs
β’ NotFree Ξ v (def_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
h2 : v β vs
β’ NotFree Ξ v (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
h2 : v β vs
β’ NotFree Ξ v (meta_var_ X) | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h2 : v β vs
h1 : False
β’ NotFree Ξ v (meta_var_ X) | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
h2 : v β vs
β’ NotFree Ξ v (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | contradiction | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h2 : v β vs
h1 : False
β’ NotFree Ξ v (meta_var_ X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : MetaVarName
vs : List VarName
h2 : v β vs
h1 : False
β’ NotFree Ξ v (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
h2 : v β vs
β’ NotFree Ξ v (pred_ X xs) | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (pred_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
h2 : v β vs
β’ NotFree Ξ v (pred_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (pred_ X xs) | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (pred_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | tauto | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (eq_ x y)
h2 : v β vs
β’ NotFree Ξ v (eq_ x y) | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ NotFree Ξ v (eq_ x y) | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (eq_ x y)
h2 : v β vs
β’ NotFree Ξ v (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ NotFree Ξ v (eq_ x y) | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ Β¬x = v β§ Β¬y = v | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ NotFree Ξ v (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | cases h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ Β¬x = v β§ Β¬y = v | case intro
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
leftβ : x β vs
rightβ : y β vs
β’ Β¬x = v β§ Β¬y = v | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1 : x β vs β§ y β vs
β’ Β¬x = v β§ Β¬y = v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | constructor | v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬x = v β§ Β¬y = v | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬x = v
case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬y = v | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬x = v β§ Β¬y = v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | intro contra | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬x = v | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬x = v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | apply h2 | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ False | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ v β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ False
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | subst contra | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ v β vs | case left
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : x β vs
β’ x β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : x = v
β’ v β vs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact h1_left | case left
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : x β vs
β’ x β vs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : x β vs
β’ x β vs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | intro contra | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬y = v | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ False | Please generate a tactic in lean4 to solve the state.
STATE:
case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
β’ Β¬y = v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | apply h2 | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ False | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ v β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ False
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | subst contra | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ v β vs | case right
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : y β vs
β’ y β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h2 : v β vs
h1_left : x β vs
h1_right : y β vs
contra : y = v
β’ v β vs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact h1_right | case right
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : y β vs
β’ y β vs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
Ξ : List (VarName Γ MetaVarName)
x y : VarName
vs : List VarName
h1_left : x β vs
h1_right : y β vs
h2 : y β vs
β’ y β vs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ NotFree Ξ v true_ | v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ True | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ NotFree Ξ v true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | simp | v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ True | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs true_
h2 : v β vs
β’ True
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
h2 : v β vs
β’ NotFree Ξ v phi.not_ | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi.not_ | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs phi.not_
h2 : v β vs
β’ NotFree Ξ v phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi.not_ | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact phi_ih vs h1 h2 | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi
β’ NotFree Ξ v phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (phi.imp_ psi)
h2 : v... | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi β§ NoM... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi β§ NoM... | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi β§ NoM... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | cases h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList vs phi β§ NoM... | case intro
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
leftβ : NoMetaVarAndAllFreeInLis... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | constructor | v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1_left : NoMetaVarAndAllFreeInList vs phi
... | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1_left : NoMetaVarAndAllFreeInLi... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List Va... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact phi_ih vs h1_left h2 | case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1_left : NoMetaVarAndAllFreeInLi... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact psi_ih vs h1_right h2 | case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
vs : List VarName
h2 : v β vs
h1_left : NoMetaVarAndAllFreeInL... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
v : VarName
Ξ : List (VarName Γ MetaVarName)
phi psi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
psi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs psi β v β vs β NotFree Ξ v psi
v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi)
h2 : v β vs
β’ NotFree Ξ v (forall_ x phi) | v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ NotFree Ξ v (forall_ x phi) | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (forall_ x phi)
h2 : v β vs
β’ NotFree Ξ v (f... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ NotFree Ξ v (forall_ x phi) | v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ x = v β¨ NotFree Ξ v phi | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ NotFree Ξ v (forall... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | by_cases c1 : x = v | v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ x = v β¨ NotFree Ξ v phi | case pos
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v
β’ x = v β¨ NotFree Ξ v phi
case neg
v : VarName
Ξ : List (VarN... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
β’ x = v β¨ NotFree Ξ v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | left | case pos
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v
β’ x = v β¨ NotFree Ξ v phi | case pos.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v
β’ x = v | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v
β’... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact c1 | case pos.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v
β’ x = v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : x = v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | right | case neg
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ x = v β¨ NotFree Ξ v phi | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ NotFree Ξ v phi | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | apply phi_ih (x :: vs) h1 | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ NotFree Ξ v phi | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x :: vs | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | simp | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x :: vs | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ Β¬v = x β§ v β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | push_neg | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ Β¬v = x β§ v β vs | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x β§ v β vs | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | constructor | case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x β§ v β vs | case neg.h.left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x
case neg.h.right
v : VarName
Ξ : List (VarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | tauto | case neg.h.left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.left
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | exact h2 | case neg.h.right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 : Β¬x = v
β’ v β vs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h.right
v : VarName
Ξ : List (VarName Γ MetaVarName)
x : VarName
phi : Formula
phi_ih : β (vs : List VarName), NoMetaVarAndAllFreeInList vs phi β v β vs β NotFree Ξ v phi
vs : List VarName
h2 : v β vs
h1 : NoMetaVarAndAllFreeInList (x :: vs) phi
c1 :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NoMetaVarAndAllFreeInList at h1 | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
h2 : v β vs
β’ NotFree Ξ v (def_ X xs) | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (def_ X xs)
h2 : v β vs
β’ NotFree Ξ v (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | unfold NotFree | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (def_ X xs) | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ NotFree Ξ v (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.all_free_in_list_and_not_in_list_imp_not_free | [572, 1] | [641, 10] | tauto | v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
Ξ : List (VarName Γ MetaVarName)
X : DefName
xs vs : List VarName
h2 : v β vs
h1 : xs β vs
β’ v β xs
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_var_set_is_empty | [644, 1] | [681, 8] | induction F generalizing vs | F : Formula
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs F
β’ F.metaVarSet = β
| case meta_var_
aβ : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ aβ)
β’ (meta_var_ aβ).metaVarSet = β
case pred_
aβΒΉ : PredName
aβ vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ aβΒΉ aβ)
β’ (pred_ aβΒΉ aβ).metaVarSet = β
case eq_
aβΒΉ aβ : VarName
vs : List VarName
h1 : NoMetaVarA... | Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs F
β’ F.metaVarSet = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_var_set_is_empty | [644, 1] | [681, 8] | case meta_var_ X =>
unfold NoMetaVarAndAllFreeInList at h1
contradiction | X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
β’ (meta_var_ X).metaVarSet = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : MetaVarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (meta_var_ X)
β’ (meta_var_ X).metaVarSet = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_var_set_is_empty | [644, 1] | [681, 8] | case pred_ X xs =>
rfl | X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
β’ (pred_ X xs).metaVarSet = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
X : PredName
xs vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (pred_ X xs)
β’ (pred_ X xs).metaVarSet = β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.no_meta_var_imp_meta_var_set_is_empty | [644, 1] | [681, 8] | case eq_ x y =>
rfl | x y : VarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (eq_ x y)
β’ (eq_ x y).metaVarSet = β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : VarName
vs : List VarName
h1 : NoMetaVarAndAllFreeInList vs (eq_ x y)
β’ (eq_ x y).metaVarSet = β
TACTIC:
|
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