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_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply forall_congr' | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | intro a | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | have s1 : Function.updateITE V (Ο.val x) a β Ο.val = Function.updateITE (V β Ο.val) x a | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (s... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply Function.updateITE_comp_right_injective | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (s... | case s1.h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply Instantiation.is_injective | case s1.h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1.h1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [β s1] | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact phi_ih (Function.updateITE V (Ο.val x) a) h1 | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (su... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' =... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | induction E | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (def_ X x... | case nil
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M [] (Ο X')) [] (def_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ Holds D I (V β ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case nil =>
unfold IsMetaVarOrAllDefInEnv at h1
simp at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M [] (Ο X')) [] (def_ X xs) β
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ Holds D I (V β βΟ) (fu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M [] (Ο X')) [] (def_ X xs) β
... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : β d β [], X = d.name β§ xs.length = d.args.length
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M [] (Ο X')) [] (de... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv [] (def_ X xs)
β’ Holds D I (V β βΟ) (fu... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : β d β [], X = d.name β§ xs.length = d.args.length
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M [] (Ο X')) [] (de... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
h1 : β d β [], X = d.name β§ xs.length = d.args.length
β’ Holds D I (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at E_ih | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
IsMetaVarOrAllDefInEnv E_tl (def_ X xs) β
(Holds D I (V β βΟ) (fun X' V' =... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
IsMetaVarOrAllDef... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | have s1 : E_hd.F.metaVarSet = β
:=
no_meta_var_imp_meta_var_set_is_empty E_hd.F E_hd.args E_hd.nf | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | split_ifs | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | case pos
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case _ c1 =>
unfold IsMetaVarOrAllDefInEnv at h1
simp at h1
cases h1
case inl c2 =>
contradiction
case inr c2 =>
unfold sub at E_ih
simp only [β E_ih c2]
apply holds_coincide_meta_var
unfold Formula.metaVarSet
simp | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | cases c1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | have s2 : Holds D I (Function.updateListITE (V β Ο.val) E_hd.args (List.map (V β Ο.val) xs)) M E_tl E_hd.F β Holds D I (Function.updateListITE V E_hd.args (List.map (V β Ο.val) xs)) M E_tl E_hd.F | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply holds_coincide_var D I (Function.updateListITE (V β Ο.val) E_hd.args (List.map (V β Ο.val) xs)) (Function.updateListITE V E_hd.args (List.map (V β Ο.val) xs)) M E_tl E_hd.F E_hd.args E_hd.nf | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | intro v a1 | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply Function.updateListITE_mem_eq_len | case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | case s2.h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [β s2] | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply holds_coincide_meta_var_no_meta_var | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact s1 | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAl... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact a1 | case s2.h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case s2.h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarO... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp | case s2.h2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | case s2.h2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2.h2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarO... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [c1_right] | case s2.h2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl,... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case s2.h2
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarO... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEnv (E_hd :: E_tl) (def_ X xs)
E_ih :
(β d β E_tl, X = d.name... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
h1 : IsMetaVarOrAllDefInEn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp at h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | cases h1 | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | case inl
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case inl c2 =>
contradiction | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case inr c2 =>
unfold sub at E_ih
simp only [β E_ih c2]
apply holds_coincide_meta_var
unfold Formula.metaVarSet
simp | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | contradiction | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub at E_ih | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = d.name β§ xs.length = d.args.length) β
(Holds D I (V β βΟ)... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)
c2 : β ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
E_ih :
(β d β E_tl, X = ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [β E_ih c2] | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)
c2 : β ... | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)
c2 : β ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | apply holds_coincide_meta_var | D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)
c2 : β ... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold Formula.metaVarSet | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)... | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp | case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVarSet = β
c1 : Β¬(X = E_hd.name β§ xs.length = E_hd.args.length)... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
M : MetaValuation D
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : DefName
xs : List VarName
V : Valuation D
E_hd : Definition
E_tl : List Definition
s1 : E_hd.F.metaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | induction F | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F : Formula
Ξ : List (VarName Γ MetaVarName)
v : VarName
h1 : NotFree Ξ v F
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
β’ IsNotFree D I M E F v | case meta_var_
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
aβ : MetaVarName
h1 : NotFree Ξ v (meta_var_ aβ)
β’ IsNotFree D I M E (meta_var_ aβ) v
case pred_
D : Type
I : Interpretation D
M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F : Formula
Ξ : List (VarName Γ MetaVarName)
v : VarName
h1 : NotFree Ξ v F
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
β’ IsNotFree D I M E F v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case meta_var_ X =>
unfold NotFree at h1
exact h2 X h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : NotFree Ξ v (meta_var_ X)
β’ IsNotFree D I M E (meta_var_ X) v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : NotFree Ξ v (meta_var_ X)
β’ IsNotFree D I M E (meta_var_ X) v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case pred_ X xs =>
unfold NotFree at h1
unfold IsNotFree
simp only [Holds]
intro V d
congr! 1
apply List.map_congr
intro x a1
have s1 : Β¬ x = v
intro contra
subst contra
contradiction
unfold Function.updateITE
simp only [if_neg s1] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : NotFree Ξ v (pred_ X xs)
β’ IsNotFree D I M E (pred_ X xs) v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : NotFree Ξ v (pred_ X xs)
β’ IsNotFree D I M E (p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case eq_ x y =>
unfold NotFree at h1
unfold IsNotFree
simp only [Holds]
intro V d
cases h1
case intro h1_left h1_right =>
simp only [Function.updateITE]
simp only [if_neg h1_left]
simp only [if_neg h1_right] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : NotFree Ξ v (eq_ x y)
β’ IsNotFree D I M E (eq_ x y) v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : NotFree Ξ v (eq_ x y)
β’ IsNotFree D I M E (eq_ x y) v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case true_ =>
unfold IsNotFree
intro V d
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ IsNotFree D I M E true_ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ IsNotFree D I M E true_ v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case not_ phi phi_ih =>
unfold NotFree at h1
unfold IsNotFree at phi_ih
unfold IsNotFree
intro V d
simp only [Holds]
congr! 1
exact phi_ih h1 V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v phi.not_
β’ IsNotFree D I M E phi.not_ v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : NotFree Ξ v (meta_var_ X)
β’ IsNotFree D I M E (meta_var_ X) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : (v, X) β Ξ
β’ IsNotFree D I M E (meta_var_ X) v | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : NotFree Ξ v (meta_var_ X)
β’ IsNotFree D I M E (meta_var_ X) v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact h2 X h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : (v, X) β Ξ
β’ IsNotFree D I M E (meta_var_ X) v | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : MetaVarName
h1 : (v, X) β Ξ
β’ IsNotFree D I M E (meta_var_ X) v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : NotFree Ξ v (pred_ X xs)
β’ IsNotFree D I M E (pred_ X xs) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ IsNotFree D I M E (pred_ X xs) v | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : NotFree Ξ v (pred_ X xs)
β’ IsNotFree D I M E (p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ IsNotFree D I M E (pred_ X xs) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), Holds D I V M E (pred_ X xs) β Holds D I (Function.updateITE V v d) M ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ IsNotFree D I M E (pred_ X xs) v
TACTI... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), Holds D I V M E (pred_ X xs) β Holds D I (Function.updateITE V v d) M ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), I X (List.map V xs) β I X (List.map (Function.updateITE V v d) xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), Holds D I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), I X (List.map V xs) β I X (List.map (Function.updateITE V v d) xs) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ I X (List.map V xs) β I X (List.map (Function.updateITE V v d) xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
β’ β (V : Valuation D) (d : D), I X (List... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ I X (List.map V xs) β I X (List.map (Function.updateITE V v d) xs) | case a.h.e'_2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ List.map V xs = List.map (Function.updateITE V v d) xs | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ I X (List.map V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | apply List.map_congr | case a.h.e'_2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ List.map V xs = List.map (Function.updateITE V v d) xs | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ β x β xs, V x = Function.updateITE V v d x | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ Li... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro x a1 | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ β x β xs, V x = Function.updateITE V v d x | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
β’ V x = Function.updateITE V v d x | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
β’ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | have s1 : Β¬ x = v | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
β’ V x = Function.updateITE V v d x | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
β’ Β¬x = v
case a.h.e'_2.a
D : Type
I : Interpre... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro contra | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
β’ Β¬x = v
case a.h.e'_2.a
D : Type
I : Interpre... | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
contra : x = v
β’ False
case a.h.e'_2.a
D : Typ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarNam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | subst contra | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
contra : x = v
β’ False
case a.h.e'_2.a
D : Typ... | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs : List VarName
V : Valuation D
d : D
x : VarName
a1 : x β xs
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
h1 : x β xs
β’ False
case a.h.e'_2.a
D : Type
I : Interpretation D
M : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarNam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | contradiction | case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs : List VarName
V : Valuation D
d : D
x : VarName
a1 : x β xs
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
h1 : x β xs
β’ False
case a.h.e'_2.a
D : Type
I : Interpretation D
M : ... | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
s1 : Β¬x = v
β’ V x = Function.updateITE ... | Please generate a tactic in lean4 to solve the state.
STATE:
case s1
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
X : PredName
xs : List VarName
V : Valuation D
d : D
x : VarName
a1 : x β xs
h2 : β (X : MetaVarName), (x, X) β Ξ β IsNotFree D I M E (meta_var_ X) x
h1 : x β x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold Function.updateITE | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
s1 : Β¬x = v
β’ V x = Function.updateITE ... | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
s1 : Β¬x = v
β’ V x = if x = v then d els... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [if_neg s1] | case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x : VarName
a1 : x β xs
s1 : Β¬x = v
β’ V x = if x = v then d els... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
X : PredName
xs : List VarName
h1 : v β xs
V : Valuation D
d : D
x ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : NotFree Ξ v (eq_ x y)
β’ IsNotFree D I M E (eq_ x y) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ IsNotFree D I M E (eq_ x y) v | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : NotFree Ξ v (eq_ x y)
β’ IsNotFree D I M E (eq_ x y) v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ IsNotFree D I M E (eq_ x y) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), Holds D I V M E (eq_ x y) β Holds D I (Function.updateITE V v d) M E (eq_ x y) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ IsNotFree D I M E (eq_ x y) v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), Holds D I V M E (eq_ x y) β Holds D I (Function.updateITE V v d) M E (eq_ x y) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), Holds D I V M E (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
V : Valuation D
d : D
β’ V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
β’ β (V : Valuation D) (d : D), V x = V y β Funct... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | cases h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
V : Valuation D
d : D
β’ V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
leftβ : Β¬x = v
rightβ : Β¬y = v
β’ V x = V y β Function.updateITE V v d x = Function.updateITE V v ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
h1 : Β¬x = v β§ Β¬y = v
V : Valuation D
d : D
β’ V x = V y β Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | case intro h1_left h1_right =>
simp only [Function.updateITE]
simp only [if_neg h1_left]
simp only [if_neg h1_right] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Function.updateITE] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β Function.updateITE V v d x = Function.updateITE V v d y | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β (if x = v then d else V x) = if y = v then d else V y | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [if_neg h1_left] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β (if x = v then d else V x) = if y = v then d else V y | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β V x = if y = v then d else V y | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [if_neg h1_right] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y β V x = if y = v then d else V y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x y : VarName
V : Valuation D
d : D
h1_left : Β¬x = v
h1_right : Β¬y = v
β’ V x = V y ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ IsNotFree D I M E true_ v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ β (V : Valuation D) (d : D), Holds D I V M E true_ β Holds D I (Function.updateITE V v d) M E true_ | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ IsNotFree D I M E true_ v
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ β (V : Valuation D) (d : D), Holds D I V M E true_ β Holds D I (Function.updateITE V v d) M E true_ | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
V : Valuation D
d : D
β’ Holds D I V M E true_ β Holds D I (Function.updateITE V v d) M E true_ | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
β’ β (V : Valuation D) (d : D), Holds D I V M E true_ β Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
V : Valuation D
d : D
β’ Holds D I V M E true_ β Holds D I (Function.updateITE V v d) M E true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
h1 : NotFree Ξ v true_
V : Valuation D
d : D
β’ Holds D I V M E true_ β Holds D I (F... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v phi.not_
β’ IsNotFree D I M E phi.not_ v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v phi
β’ IsNotFree D I M E phi.not_ v | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at phi_ih | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v phi
β’ IsNotFree D I M E phi.not_ v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v p... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
h1 : ... | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact phi_ih h1 V d | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
psi_ih : NotFree Ξ v psi β IsNotFree D I M E psi v
h1 : NotFree Ξ v (phi.im... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
psi_ih : NotFree Ξ v psi β IsNotFree D I M E psi v
h1 : NotFree Ξ v phi β§ N... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
psi_ih : NotFr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at phi_ih | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
psi_ih : NotFree Ξ v psi β IsNotFree D I M E psi v
h1 : NotFree Ξ v phi β§ N... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
psi_ih : NotFr... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at psi_ih | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | cases h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M E phi
p... | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact phi_ih h1_left V d | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | exact psi_ih h1_right V d | case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
phi psi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold NotFree at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : NotFree Ξ v (forall_ x phi)
β’ IsNotFree D I M E (forall_ x phi... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : x = v β¨ NotFree Ξ v phi
β’ IsNotFree D I M E (forall_ x phi) v | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : N... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree at phi_ih | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : x = v β¨ NotFree Ξ v phi
β’ IsNotFree D I M E (forall_ x phi) v | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih : NotFree Ξ v phi β IsNotFree D I M E phi v
h1 : x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | unfold IsNotFree | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro V d | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | apply forall_congr' | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V v d) M... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D),... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | intro d' | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | by_cases c1 : x = v | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE V... | case pos
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.not_free_imp_is_not_free | [1604, 1] | [1734, 26] | cases h1 | case pos
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updateITE... | case pos.inl
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D) (d : D), Holds D I V M E phi β Holds D I (Function.updat... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
v : VarName
h2 : β (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
x : VarName
phi : Formula
phi_ih :
NotFree Ξ v phi β β (V : Valuation D)... |
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