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.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | apply Exists.intro d | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : Definition
E... | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : Definition
E... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl,... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | constructor | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : Definition
E... | case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : De... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl,... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | simp | case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : De... | case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : De... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | right | case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : De... | case left.h
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : ... | Please generate a tactic in lean4 to solve the state.
STATE:
case left
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | exact E_ih_1_left | case left.h
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case left.h
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.def_holds_imp_def_in_env | [1287, 1] | [1320, 29] | exact E_ih_1_right | case right
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : β d β E_tl, name = d.name β§ args.length = d.args.length
d : D... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case right
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
name : DefName
args : List VarName
E_hd : Definition
E_tl : List Definition
c1 : Β¬(name = E_hd.name β§ args.length = E_hd.args.length)
h1 : Holds D I V M E_tl (def_ name args)
E_ih : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | induction F generalizing V | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E E' : Env
F : Formula
h1 : β E1, E' = E1 ++ E
h2 : IsMetaVarOrAllDefInEnv E F
h3 : E'.Nodup
β’ Holds D I V M E' F β Holds D I V M E F | case meta_var_
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
aβ : MetaVarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (meta_var_ aβ)
β’ Holds D I V M E' (meta_var_ aβ) β Holds D I V M E (meta_var_ aβ)
case pred_
D : Type
I : Interpretation D
M : MetaValuation D... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E E' : Env
F : Formula
h1 : β E1, E' = E1 ++ E
h2 : IsMetaVarOrAllDefInEnv E F
h3 : E'.Nodup
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_coincide_env | [1379, 1] | [1462, 35] | case meta_var_ X =>
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : MetaVarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I V M E' (meta_var_ X) β Holds D I V M E (meta_var_ X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : MetaVarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I V M E' (meta_var_ X) β Holds D I V M E (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case pred_ X xs =>
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : PredName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I V M E' (pred_ X xs) β Holds D I V M E (pred_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : PredName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I V M E' (pred_ X xs) β Holds D I V M E (pred_ X xs)
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case eq_ x y =>
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x y : VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I V M E' (eq_ x y) β Holds D I V M E (eq_ x y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x y : VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I V M E' (eq_ x y) β Holds D I V M E (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case true_ =>
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I V M E' true_ β Holds D I V M E true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I V M E' true_ β Holds D I V M E true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case not_ phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h2
simp only [Holds]
congr! 1
exact phi_ih V h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi.not_
β’ Holds D I V M E' phi.not_ β Holds D I V M E ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case forall_ x phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h2
simp only [Holds]
apply forall_congr'
intro a
exact phi_ih (Function.updateITE V x a) h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (forall_ x 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 E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaV... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : MetaVarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I V M E' (meta_var_ X) β Holds D I V M E (meta_var_ X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : MetaVarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I V M E' (meta_var_ X) β Holds D I V M E (meta_var_ X)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : PredName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I V M E' (pred_ X xs) β Holds D I V M E (pred_ X xs) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : PredName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I V M E' (pred_ X xs) β Holds D I V M E (pred_ X xs)
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x y : VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I V M E' (eq_ x y) β Holds D I V M E (eq_ x y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x y : VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I V M E' (eq_ x y) β Holds D I V M E (eq_ x y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I V M E' true_ β Holds D I V M E true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I V M E' true_ β Holds D I V M E true_
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | unfold IsMetaVarOrAllDefInEnv at h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi.not_
β’ Holds D I V M E' phi.not_ β Holds D I V M E ... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' phi.not_ β Holds D I V M E phi.n... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' phi.not_ β Holds D I V M E phi.n... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Β¬Holds D I V M E' phi β Β¬Holds D I V M E phi | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Β¬Holds D I V M E' phi β Β¬Holds D I V M E phi | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' phi β Holds D I ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefIn... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact phi_ih V h2 | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' phi β Holds D I ... | 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 E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsM... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | unfold IsMetaVarOrAllDefInEnv at h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMeta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | cases h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β H... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMeta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMeta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β Holds D I V ... | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β H... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMeta... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact phi_ih V h2_left | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β H... | 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 E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact psi_ih V h2_right | case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E psi β (Holds D I V M E' psi β ... | 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 E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
phi psi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
psi_ih : β (V : Valuatio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | unfold IsMetaVarOrAllDefInEnv at h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (forall_ x phi)
β’ Holds D I V M E' (forall_... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' (forall_ x phi) β Ho... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaV... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ Holds D I V M E' (forall_ x phi) β Ho... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ (β (d : D), Holds D I (Function.updat... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaV... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | apply forall_congr' | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ (β (d : D), Holds D I (Function.updat... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ β (a : D), Holds D I (Function... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaV... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | intro a | case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
β’ β (a : D), Holds D I (Function... | case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
a : D
β’ Holds D I (Function.upda... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact phi_ih (Function.updateITE V x a) h2 | case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E phi
a : D
β’ Holds D I (Function.upda... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
x : VarName
phi : Formula
phi_ih : β (V : Valuation D), IsMetaVarOrAllDefInEnv E phi β (Holds D I V M E' phi β Holds D I V M E phi)
V : Valuation D
h2 : ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | apply Exists.elim h1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ β (a : Env), E' = a ++ E β (Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | intro E1 h1_1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ β (a : Env), E' = a ++ E β (Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs)) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
β’ β (a : Env), E' = a ++ E β (Holds D I V M E' (def_ X xs) β Holds D I V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | clear h1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h1 : β E1, E' = E1 ++ E
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | unfold IsMetaVarOrAllDefInEnv at h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
h2 : IsMetaVarOrAllDefInEnv E (def_ X xs)
E1 : Env
h1_1 : E' = E1 ++ E
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs)
TACTIC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | apply Exists.elim h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β (a : Definition),
a β E β§ X = a.name β§ xs.length = a.args.length β (Holds D I V M E' (def_ X xs) β Holds D I ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | intro a h2_1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β (a : Definition),
a β E β§ X = a.name β§ xs.length = a.args.length β (Holds D I V M E' (def_ X xs) β Holds D I ... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
β’ β (a : Definition),
a β E β§ X = a.name β§ xs.length... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | clear h2 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E... | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
h2 : β d β E, X = d.name β§ xs.length = d.args.length
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | unfold Env.Nodup at h3 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D I V M E (def_ X xs) | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E'... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : E'.Nodup
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E' (def_ X xs) β Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | cases h2_1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β E β§ X = a.name β§ xs.length = a.args.length
β’ Holds D I V M E'... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
leftβ : a β E
rightβ : X = a.name β§ xs.length = a.args.length... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1 : a β ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | cases h2_1_right | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1_left : a β E
h2_1_right : X = a.name β§ xs.length = a.args.length
β’ ... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1_left : a β E
leftβ : X = a.name
rightβ : xs.length = a.a... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1_left :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | subst h1_1 | D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.len... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) (E1 ++... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E E' : Env
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) E'
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
h1_1 : E' = E1 ++ E
a : Definition
h2_1_left :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | induction E1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) (E1 ++... | case nil
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) ([] ++... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
E1 : Env
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case nil =>
simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) ([] ++ E)
β’ Hol... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.na... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.length = d2.args.length β False) ([] ++ E)
β’ Hol... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
h3 : List.Pairwise (fun d1 d2 => d1.name = d2.na... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp at h3 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | cases h3 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | split_ifs | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | case pos
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | case _ c1 =>
exact E1_ih h3_right | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | cases c1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exfalso | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | apply h3_left a | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | right | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | case a.h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definitio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact h2_1_left | case a.h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definit... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [β h2_1_right_left] | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definitio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [c1_left] | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definitio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [β h2_1_right_right] | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definitio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | simp only [c1_right] | case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definitio... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_coincide_env | [1379, 1] | [1462, 35] | exact E1_ih h3_right | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih :
List.Pairwise (fun d1 d2 => d1.name = d2.name β d1.args.... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
X : DefName
xs : List VarName
V : Valuation D
a : Definition
h2_1_left : a β E
h2_1_right_left : X = a.name
h2_1_right_right : xs.length = a.args.length
E1_hd : Definition
E1_tl : List Definition
E1_ih... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | induction F generalizing V | D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E F
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E F β Holds D I V M E (sub Ο Ο F) | case meta_var_
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
aβ : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ aβ)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (met... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V : Valuation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
F : Formula
h1 : IsMetaVarOrAllDefInEnv E F
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case meta_var_ X =>
cases h2
case intro h2_left h2_right =>
unfold sub
simp only [Holds]
simp only [Function.comp.assoc]
simp only [h2_left]
simp only [Function.comp_id] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_var_ X) β
H... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I (V β βΟ) (fun X' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case pred_ X xs =>
unfold sub
simp only [Holds]
simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (pred_ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case eq_ x y =>
unfold sub
simp only [Holds]
simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (eq_ x y) β Holds D I V M E... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case true_ =>
unfold sub
simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E true_ β Holds D I V M E (sub Ο Ο true_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case not_ phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h1
unfold sub
simp only [Holds]
congr! 1
exact phi_ih V h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case forall_ x phi phi_ih =>
unfold IsMetaVarOrAllDefInEnv at h1
cases h2
case intro h2_left h2_right =>
unfold sub
simp only [Holds]
apply forall_congr'
intro a
have s1 : Function.updateITE V (Ο.val x) a β Ο.val = Function.updateITE (V β Ο.val) x a
apply Function.updateITE_comp_right_inje... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | cases h2 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_var_ X) β
H... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
leftβ : βΟ β Ο' = id
rightβ : Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
β’ Holds D I (V β βΟ) (fun X' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case intro h2_left h2_right =>
unfold sub
simp only [Holds]
simp only [Function.comp.assoc]
simp only [h2_left]
simp only [Function.comp_id] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_v... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_v... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (meta_v... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I ((V β βΟ) β Ο') M E (Ο X) β Holds D I V M E (Ο X) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Function.comp.assoc] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I ((V β βΟ) β Ο') M E (Ο X) β Holds D I V M E (Ο X) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ β Ο') M E (Ο X) β Holds D I V M E (Ο X) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I ((V... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [h2_left] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β βΟ β Ο') M E (Ο X) β Holds D I V M E (Ο X) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β id) M E (Ο X) β Holds D I V M E (Ο X) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Function.comp_id] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V β id) M E (Ο X) β Holds D I V M E (Ο X) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
X : MetaVarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (meta_var_ X)
h2_left : βΟ β Ο' = id
h2_right : Ο' β βΟ = id
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (pred_ ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (pred_ ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (pred_ ... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ I X (List.map (V β βΟ) xs) β I X (List.map V (List.map (βΟ) xs)) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ I X (List.map (V β βΟ) xs) β I X (List.map V (List.map (βΟ) xs)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
X : PredName
xs : List VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (pred_ X xs)
β’ I X (List.map... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (eq_ x y) β Holds D I V M E... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (eq_ x y) β Holds D I V M E... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E (eq_ x y) β Holds D I V M E... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ (V β βΟ) x = (V β βΟ) y β V (βΟ x) = V (βΟ y) | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ Holds D I (V β βΟ) (fun X' V' => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ (V β βΟ) x = (V β βΟ) y β V (βΟ x) = V (βΟ y) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x y : VarName
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E (eq_ x y)
β’ (V β βΟ) x = (V β βΟ) y β V (βΟ x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E true_ β Holds D I V M E (sub Ο Ο true_) | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E true_ β Holds D I V M E true_ | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E true_ β Holds D I V M E true_ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
V : Valuation D
h1 : IsMetaVarOrAllDefInEnv E true_
β’ Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds... | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X'... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact phi_ih V h1 | case a.h.e'_1.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X'... | 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
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(H... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | cases h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | simp only [Holds] | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | congr! 1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β H... | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact phi_ih V h1_left | case a.h.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')... | 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
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | exact psi_ih V h1_right | case a.h'.a
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X'... | 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
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
phi psi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(H... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold IsMetaVarOrAllDefInEnv at h1 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | cases h2 | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E... | case intro
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
h2 : βΟ β Ο' = id β§ Ο' β βΟ = id
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | case intro h2_left h2_right =>
unfold sub
simp only [Holds]
apply forall_congr'
intro a
have s1 : Function.updateITE V (Ο.val x) a β Ο.val = Function.updateITE (V β Ο.val) x a
apply Function.updateITE_comp_right_injective
apply Instantiation.is_injective
simp only [β s1]
exact phi_ih (Function.updateI... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/MM0/MM0.lean | MM0.holds_sub | [1465, 1] | [1577, 15] | unfold sub | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds D I (V' β Ο') M E (Ο X')) E phi β Holds D I V M E (sub Ο Ο p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
M : MetaValuation D
E : Env
Ο : Instantiation
Ο' : VarName β VarName
Ο : MetaInstantiation
x : VarName
phi : Formula
phi_ih :
β (V : Valuation D),
IsMetaVarOrAllDefInEnv E phi β
(Holds D I (V β βΟ) (fun X' V' => Holds... |
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