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.lem_4 | [1935, 1] | [1999, 21] | case _ c1 =>
cases h2
case inl c2 =>
subst c2
simp at c1
cases h3
case intro h3_left h3_right =>
exfalso
exact c1 h3_left h3_right
case inr c2 =>
specialize ih h1_right_right c2
simp only [β ih]
apply holds_coincide_env D I (Function.updateListITE V d.args (List.map V args)... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case inl
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | case inl c2 =>
subst c2
exact holds_coincide_env D I (Function.updateListITE V d.args (List.map V args)) M tl (d :: tl) d.F s2 h1_right_left s1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | subst c2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exact holds_coincide_env D I (Function.updateListITE V d.args (List.map V args)) M tl (d :: tl) d.F s2 h1_right_left s1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.update... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h3 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case intro
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases c1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : Env.Nod... | case intro
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exfalso | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : Env.Nod... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : Env.Nod... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | apply h1_left d c2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : Env.Nod... | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp only [β c1_left] | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exact h3_left | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp only [β c1_right] | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exact h3_right | case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
s1 : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | case inl
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | case inl c2 =>
subst c2
simp at c1
cases h3
case intro h3_left h3_right =>
exfalso
exact c1 h3_left h3_right | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | case inr c2 =>
specialize ih h1_right_right c2
simp only [β ih]
apply holds_coincide_env D I (Function.updateListITE V d.args (List.map V args)) M tl (hd :: tl) d.F s2
apply def_in_well_formed_env_is_meta_var_or_all_def_in_env tl d h1_right_right c2
exact s1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | subst c2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp at c1 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.update... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | cases h3 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M ... | case intro
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
h1_right_right : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.update... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | case intro h3_left h3_right =>
exfalso
exact c1 h3_left h3_right | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
h1_right_right : Env.WellFor... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exfalso | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
h1_right_right : Env.WellFor... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
h1_right_right : Env.WellFor... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exact c1 h3_left h3_right | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Holds D I V M tl (def_ name args))
h1_right_right : Env.WellFor... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F β Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | specialize ih h1_right_right c2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I (Function.updateListITE V d.args (List.map V args)) M tl d.F ... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
ih :
Env.WellFormed tl β
d β tl β
(Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | simp only [β ih] | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | apply holds_coincide_env D I (Function.updateListITE V d.args (List.map V args)) M tl (hd :: tl) d.F s2 | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.length = d'.... | case h2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.leng... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | apply def_in_well_formed_env_is_meta_var_or_all_def_in_env tl d h1_right_right c2 | case h2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.leng... | case h3
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.leng... | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.lem_4 | [1935, 1] | [1999, 21] | exact s1 | case h3
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E1 ++ tl
h1_left : β d' β tl, hd.name = d'.name β hd.args.leng... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h3
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
d : Definition
name : DefName
args : List VarName
h3 : name = d.name β§ args.length = d.args.length
hd : Definition
tl : List Definition
s1 : Env.Nodup (hd :: tl)
s2 : β E1, hd :: tl = E... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | induction h2 generalizing V | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2 : IsConv E F F'
β’ Holds D I V M E F β Holds D I V M E F' | case conv_refl
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
phiβ : Formula
V : Valuation D
β’ Holds D I V M E phiβ β Holds D I V M E phiβ
case conv_symm
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
phiβ phi'β : Formula
aβ : IsCo... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2 : IsConv E F F'
β’ Holds D I V M E F β Holds D I V M E F'
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_refl h2_phi =>
rfl | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi : Formula
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi : Formula
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_symm h2_phi h2_phi' _ h2_ih =>
symm
exact h2_ih V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi' β Holds D I V M E h2_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_trans h2_phi h2_phi' h2_phi'' _ _ h2_ih_1 h2_ih_2 =>
trans Holds D I V M E h2_phi'
exact h2_ih_1 V
exact h2_ih_2 V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_not h2_phi h2_phi' _ h2_ih =>
simp only [Holds]
congr! 1
exact h2_ih V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi.not_ β Holds D I V M E h2_phi'.not_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_forall h2_x h2_phi h2_phi' _ h2_ih =>
simp only [Holds]
apply forall_congr'
intro a
exact h2_ih (Function.updateITE V h2_x a) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E (forall_ h2_x h2_phi) β Holds D I V M E (forall_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Hol... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | case conv_unfold d Ο h2 =>
obtain β¨Ο', a1β© := Ο.2
have s1 : IsMetaVarOrAllDefInEnv E d.F := def_in_well_formed_env_is_meta_var_or_all_def_in_env E d h1 h2
simp only [β holds_sub D I V M E Ο Ο' meta_var_ d.F s1 a1]
clear s1
have s2 : d.name = d.name β§ (List.map Ο.val d.args).length = d.args.length
simp
sim... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | rfl | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi : Formula
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi : Formula
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | symm | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi' β Holds D I V M E h2_phi | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi' | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | trans Holds D I V M E h2_phi' | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih_1 V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih_2 V | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_phi'... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_phi'' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_phi' h2_phi''
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi.not_ β Holds D I V M E h2_phi'.not_ | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Β¬Holds D I V M E h2_phi β Β¬Holds D I V M E h2_phi' | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Β¬Holds D I V M E h2_phi β Β¬Holds D I V M E h2_phi' | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi' | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Β¬Holds D I V M E h... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih V | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E h2_phi β Holds D I V M E h2_phi' | 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
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D I V M E h2_... | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds D ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih_1 V | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds 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
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒΉ : IsConv E h2_phi h2_phi'
aβ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih_2 V | case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒ² : IsConv E h2_phi h2_phi'
aβΒΉ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
h2_ih_2 : β (V : Valuation D), Holds ... | 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
F F' : Formula
h1 : E.WellFormed
h2_phi h2_phi' h2_psi h2_psi' : Formula
aβΒ² : IsConv E h2_phi h2_phi'
aβΒΉ : IsConv E h2_psi h2_psi'
h2_ih_1 : β (V : Valuation D), Holds D I V M E h2_phi β ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Holds D I V M E (forall_ h2_x h2_phi) β Holds D I V M E (forall_... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ (β (d : D), Holds D I (Function.updateITE V h2_x d) M E h2_phi) ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ Hol... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | apply forall_congr' | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ (β (d : D), Holds D I (Function.updateITE V h2_x d) M E h2_phi) ... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ β (a : D), Holds D I (Function.updateITE V h2_x a) M E h2... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ (β ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | intro a | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
β’ β (a : D), Holds D I (Function.updateITE V h2_x a) M E h2... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
a : D
β’ Holds D I (Function.updateITE V h2_x a) M E h2_phi ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact h2_ih (Function.updateITE V h2_x a) | case h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation D
a : D
β’ Holds D I (Function.updateITE V h2_x a) M E h2_phi ... | 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
F F' : Formula
h1 : E.WellFormed
h2_x : VarName
h2_phi h2_phi' : Formula
aβ : IsConv E h2_phi h2_phi'
h2_ih : β (V : Valuation D), Holds D I V M E h2_phi β Holds D I V M E h2_phi'
V : Valuation ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | obtain β¨Ο', a1β© := Ο.2 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F) | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | have s1 : IsMetaVarOrAllDefInEnv E d.F := def_in_well_formed_env_is_meta_var_or_all_def_in_env E d h1 h2 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V M E (sub Ο meta_var_ d.F) | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [β holds_sub D I V M E Ο Ο' meta_var_ d.F s1 a1] | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β Holds D I V... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β
Holds D... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | clear s1 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β
Holds D... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β
Holds D I (V β βΟ) (fun X' V' => Holds D ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s1 : IsMetaVarOrAllDefInEnv E d.F
β’ Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | have s2 : d.name = d.name β§ (List.map Ο.val d.args).length = d.args.length | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map (βΟ) d.args)) β
Holds D I (V β βΟ) (fun X' V' => Holds D ... | case s2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
case intro
D : Type
I : Interpretation... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I V M E (def_ d.name (List.map ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp | case s2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
case intro
D : Type
I : Interpretation... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
β’ Holds D I V M E (def_ d.name (L... | Please generate a tactic in lean4 to solve the state.
STATE:
case s2
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ d.name = d.name β§ (List.map (βΟ) d.args).l... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [β lem_4 D I V M E d d.name (List.map Ο.val d.args) h1 h2 s2] | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
β’ Holds D I V M E (def_ d.name (L... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
β’ Holds D I (Function.updateListI... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | clear s2 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.args).length = d.args.length
β’ Holds D I (Function.updateListI... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args))) M E d.F β
Holds ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s2 : d.name = d.name β§ (List.map (βΟ) d.a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | have s3 : d.F.metaVarSet = β
:= no_meta_var_imp_meta_var_set_is_empty d.F d.args d.nf | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args))) M E d.F β
Holds ... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp only [holds_coincide_meta_var_no_meta_var D I (V β Ο.val) (fun (X' : MetaVarName) (V' : Valuation D) => Holds D I (V' β Ο') M E (meta_var_ X')) M E d.F s3] | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Func... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | clear s3 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args))) M E d.F β Holds D I ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
s3 : d.F.metaVarSet = β
β’ Holds D I (Func... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | apply holds_coincide_var D I (Function.updateListITE V d.args (List.map V (List.map Ο.val d.args))) (V β Ο.val) M E d.F d.args d.nf | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args))) M E d.F β Holds D I ... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ β v β d.args, Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args)) v = (V β βΟ) v | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (Function.updateListITE V d.a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | intro v a2 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ β v β d.args, Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args)) v = (V β βΟ) v | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args)) v = ... | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ β v β d.args, Function.updateListITE V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | simp | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.updateListITE V d.args (List.map V (List.map (βΟ) d.args)) v = ... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.updateListITE V d.args (List.map (V β βΟ) d.args) v = V (βΟ v) | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.up... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_conv | [2002, 1] | [2057, 67] | exact Function.updateListITE_map_mem V (V β Ο.val) d.args v a2 | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.updateListITE V d.args (List.map (V β βΟ) d.args) v = V (βΟ v) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
F F' : Formula
h1 : E.WellFormed
d : Definition
Ο : Instantiation
h2 : d β E
V : Valuation D
Ο' : VarName β VarName
a1 : βΟ β Ο' = id β§ Ο' β βΟ = id
v : VarName
a2 : v β d.args
β’ Function.up... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | induction h1 generalizing M | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h1 : IsProof E Ξ Ξ F
h2 : E.WellFormed
nf : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F : Formula) (V : Valuation D), F β Ξ β Holds D I V M E F
β’ β (V ... | case hyp
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
Ξβ : List (VarName Γ MetaVarName)
Ξβ : List Formula
phiβ : Formula
aβΒΉ : IsMetaVarOrAllDefInEnv E phiβ
aβ : phiβ β Ξβ
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β Ξβ β I... | 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)
Ξ : List Formula
F : Formula
h1 : IsProof E Ξ Ξ F
h2 : E.WellFormed
nf : β (v : VarName) (X : MetaVarName), (v, X) β Ξ β IsNotFree D I M E (meta_var_ X) v
hyp : β (F : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case hyp h1_Ξ h1_Ξ h1_phi h1_1 h1_2 =>
intro V
exact hyp h1_phi V h1_2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : Meta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case mp h1_Ξ h1_Ξ h1_phi h1_psi h1_1 h1_2 h1_ih_1 h1_ih_2 =>
simp only [Holds] at h1_ih_2
intro V
exact h1_ih_2 M nf hyp V (h1_ih_1 M nf hyp V) | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case prop_1 h1_Ξ h1_Ξ h1_phi h1_psi h1_1 h1_2 =>
simp only [Holds]
intro V a1 a2
exact a1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case prop_2 h1_Ξ h1_Ξ h1_phi h1_psi h1_chi h1_1 h1_2 h1_3 =>
simp only [Holds]
intro V a1 a2 a3
apply a1 a3
exact a2 a3 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case prop_3 h1_Ξ h1_Ξ h1_phi h1_psi h1_1 h1_2 =>
simp only [Holds]
intro V a1 a2
by_contra contra
exact a1 contra a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case gen h1_Ξ h1_Ξ h1_phi h1_x h1_1 h1_ih =>
simp only [Holds]
intro V d
exact h1_ih M nf hyp (Function.updateITE V h1_x d) | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : Me... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case pred_1 h1_Ξ h1_Ξ h1_phi h1_psi h1_x h1_1 h1_2 =>
simp only [Holds]
intro V a1 a2 d
apply a1 d
exact a2 d | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case pred_2 h1_Ξ h1_Ξ h1_phi h1_x h1_1 h1_2 =>
have s1 : IsNotFree D I M E h1_phi h1_x
apply not_free_imp_is_not_free D I M E h1_phi h1_Ξ h1_x h1_2
exact nf h1_x
simp only [Holds]
intro V a1 a
unfold IsNotFree at s1
simp only [β s1 V a]
exact a1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree h1_Ξ h1_x h1_phi
M : MetaValuation D
nf : β (v : VarName) (X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : NotFree... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case eq_1 h1_Ξ h1_Ξ h1_x h1_y h1_1 =>
unfold exists_
simp only [Holds]
simp
intro V
apply Exists.intro (V h1_y)
unfold Function.updateITE
simp | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree D I M E (meta_var_ X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_x h1_y : VarName
h1_1 : Β¬h1_y = h1_x
M : MetaValuation D
nf : β (v : VarName) (X :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case eq_3 h1_Ξ h1_Ξ h1_n h1_name h1_xs h1_ys =>
sorry | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_n : β
h1_name : PredName
h1_xs h1_ys : Fin h1_n β VarName
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β h1_Ξ β IsNotFree... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_n : β
h1_name : PredName
h1_xs h1_ys : Fin h1_n β VarName
M : MetaValuation D
nf :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | case conv h1_Ξ h1_Ξ h1_phi h1_phi' h1_1 h1_2 h1_3 h1_ih =>
intro V
have s1 : Holds D I V M E h1_phi := h1_ih M nf hyp V
simp only [β holds_conv D I V M E h1_phi h1_phi' h2 h1_3]
exact s1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_3 : IsConv E h1_phi h1_phi'
h1_ih :
β (M :... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_phi' : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi'
h1_2 : IsProof E h1_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : Meta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact hyp h1_phi V h1_2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : MetaValuation D
nf : β (v : VarName) (X : MetaVarName), (v, X) β ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : h1_phi β h1_Ξ
M : Meta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] at h1_ih_2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact h1_ih_2 M nf hyp V (h1_ih_1 M nf hyp V) | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ (h1_phi.imp_ h1_psi)
h1_ih_1 :
β (M : MetaValuation D),
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_2 : IsProof E h1_Ξ h1_Ξ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact a1 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a2 a3 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply a1 a3 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact a2 a3 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
h1_3 : IsMetaVarOrAllDefInEnv E h1_ch... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi h1_chi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | by_contra contra | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact a1 contra a2 | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v : VarName) (X ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllD... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : Me... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V d | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : Me... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | exact h1_ih M nf hyp (Function.updateITE V h1_x d) | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : MetaValuation D),
(β (v : VarName) (X : MetaVarName), (v, X... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi : Formula
h1_x : VarName
h1_1 : IsProof E h1_Ξ h1_Ξ h1_phi
h1_ih :
β (M : Me... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | simp only [Holds] | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | intro V a1 a2 d | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_is_proof | [2060, 1] | [2162, 13] | apply a1 d | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : IsMetaVarOrAllDefInEnv E h1_psi
M : MetaValuation D
nf : β (v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
E : Env
Ξ : List (VarName Γ MetaVarName)
Ξ : List Formula
F : Formula
h2 : E.WellFormed
h1_Ξ : List (VarName Γ MetaVarName)
h1_Ξ : List Formula
h1_phi h1_psi : Formula
h1_x : VarName
h1_1 : IsMetaVarOrAllDefInEnv E h1_phi
h1_2 : ... |
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