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/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | all_goals
simp only [predVarOccursIn]
simp only [Formula.predVarSet] | case pred_const_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ predVarOccursIn P n (pred_const_ aβΒΉ aβ) β (P, n) β (pred_const_ aβΒΉ aβ).predVarSet
case pred_var_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ predVarOccursIn P n (pred_var_ aβΒΉ aβ) β (P, n) β (pred_var_ aβΒΉ aβ).predVarSet
case eq_
P : P... | case pred_const_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ False β (P, n) β β
case pred_var_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ P = aβΒΉ β§ n = aβ.length β (P, n) β {(aβΒΉ, aβ.length)}
case eq_
P : PredName
n : β
aβΒΉ aβ : VarName
β’ False β (P, n) β β
case true_
P : PredName
n : β
β’ False ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ predVarOccursIn P n (pred_const_ aβΒΉ aβ) β (P, n) β (pred_const_ aβΒΉ aβ).predVarSet
case pred_var_
P : PredName
n : β
aβΒΉ : PredName
aβ : List VarName
β’ predVarOccursIn P n (pred_var_ aβΒΉ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case pred_const_ X xs | pred_var_ X xs | def_ X xs =>
simp | P : PredName
n : β
X : DefName
xs : List VarName
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
X : DefName
xs : List VarName
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case eq_ x y =>
simp | P : PredName
n : β
x y : VarName
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
x y : VarName
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case true_ | false_ =>
tauto | P : PredName
n : β
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case not_ phi phi_ih =>
tauto | P : PredName
n : β
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case
imp_ phi psi phi_ih psi_ih
| and_ phi psi phi_ih psi_ih
| or_ phi psi phi_ih psi_ih
| iff_ phi psi phi_ih psi_ih =>
simp
tauto | P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet βͺ psi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet βͺ psi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
tauto | P : PredName
n : β
x : VarName
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
x : VarName
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | simp only [predVarOccursIn] | case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ predVarOccursIn P n (def_ aβΒΉ aβ) β (P, n) β (def_ aβΒΉ aβ).predVarSet | case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ False β (P, n) β (def_ aβΒΉ aβ).predVarSet | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ predVarOccursIn P n (def_ aβΒΉ aβ) β (P, n) β (def_ aβΒΉ aβ).predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | simp only [Formula.predVarSet] | case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ False β (P, n) β (def_ aβΒΉ aβ).predVarSet | case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ False β (P, n) β β
| Please generate a tactic in lean4 to solve the state.
STATE:
case def_
P : PredName
n : β
aβΒΉ : DefName
aβ : List VarName
β’ False β (P, n) β (def_ aβΒΉ aβ).predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | simp | P : PredName
n : β
X : DefName
xs : List VarName
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
X : DefName
xs : List VarName
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | simp | P : PredName
n : β
x y : VarName
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
x y : VarName
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | tauto | P : PredName
n : β
β’ False β (P, n) β β
| no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
β’ False β (P, n) β β
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | tauto | P : PredName
n : β
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | simp | P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet βͺ psi.predVarSet | P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet β¨ (P, n) β psi.predVarSet | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet βͺ psi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | tauto | P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet β¨ (P, n) β psi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
phi psi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
psi_ih : predVarOccursIn P n psi β (P, n) β psi.predVarSet
β’ predVarOccursIn P n phi β¨ predVarOccursIn P n psi β (P, n) β phi.predVarSet β¨ (P, n) β psi.predVarSet
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.predVarOccursIn_iff_mem_predVarSet | [438, 1] | [464, 10] | tauto | P : PredName
n : β
x : VarName
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : PredName
n : β
x : VarName
phi : Formula
phi_ih : predVarOccursIn P n phi β (P, n) β phi.predVarSet
β’ predVarOccursIn P n phi β (P, n) β phi.predVarSet
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | induction F | v : VarName
F : Formula
h1 : isBoundIn v F
β’ occursIn v F | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : isBoundIn v (eq_ aβΒΉ aβ... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
F : Formula
h1 : isBoundIn v F
β’ occursIn v F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | all_goals
simp only [isBoundIn] at h1 | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : isBoundIn v (eq_ aβΒΉ aβ... | case not_
v : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβ
β’ occursIn v aβ.not_
case imp_
v : VarName
aβΒΉ aβ : Formula
a_ihβΒΉ : isBoundIn v aβΒΉ β occursIn v aβΒΉ
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβΒΉ β¨ isBoundIn v aβ
β’ occursIn v (aβΒΉ.imp_ aβ)
case and_
v : VarN... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isBoundIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | all_goals
simp only [occursIn]
tauto | case not_
v : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβ
β’ occursIn v aβ.not_
case imp_
v : VarName
aβΒΉ aβ : Formula
a_ihβΒΉ : isBoundIn v aβΒΉ β occursIn v aβΒΉ
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβΒΉ β¨ isBoundIn v aβ
β’ occursIn v (aβΒΉ.imp_ aβ)
case and_
v : VarN... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case not_
v : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβ
β’ occursIn v aβ.not_
case imp_
v : VarName
aβΒΉ aβ : Formula
a_ihβΒΉ : isBoundIn v aβΒΉ β occursIn v aβΒΉ
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : isBoundIn v aβΒΉ β¨ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | simp only [isBoundIn] at h1 | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : isBoundIn v (def_ aβΒΉ aβ)
β’ occursIn v (def_ aβΒΉ aβ) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : isBoundIn v (def_ aβΒΉ aβ)
β’ occursIn v (def_ aβΒΉ aβ)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | simp only [occursIn] | case exists_
v aβΒΉ : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : v = aβΒΉ β¨ isBoundIn v aβ
β’ occursIn v (exists_ aβΒΉ aβ) | case exists_
v aβΒΉ : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : v = aβΒΉ β¨ isBoundIn v aβ
β’ v = aβΒΉ β¨ occursIn v aβ | Please generate a tactic in lean4 to solve the state.
STATE:
case exists_
v aβΒΉ : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : v = aβΒΉ β¨ isBoundIn v aβ
β’ occursIn v (exists_ aβΒΉ aβ)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isBoundIn_imp_occursIn | [467, 1] | [478, 10] | tauto | case exists_
v aβΒΉ : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : v = aβΒΉ β¨ isBoundIn v aβ
β’ v = aβΒΉ β¨ occursIn v aβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case exists_
v aβΒΉ : VarName
aβ : Formula
a_ihβ : isBoundIn v aβ β occursIn v aβ
h1 : v = aβΒΉ β¨ isBoundIn v aβ
β’ v = aβΒΉ β¨ occursIn v aβ
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | induction F | v : VarName
F : Formula
h1 : isFreeIn v F
β’ occursIn v F | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : isFreeIn v (eq_ aβΒΉ aβ)
β’... | Please generate a tactic in lean4 to solve the state.
STATE:
v : VarName
F : Formula
h1 : isFreeIn v F
β’ occursIn v F
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | all_goals
simp only [isFreeIn] at h1 | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : isFreeIn v (eq_ aβΒΉ aβ)
β’... | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : v = aβΒΉ β¨ v = aβ
β’ occursIn v (eq_ aβΒΉ aβ)
case not_
v : VarName
aβ : Fo... | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_const_ aβΒΉ aβ)
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : isFreeIn v (pred_var_ aβΒΉ aβ)
β’ occursIn v (pred_var_ aβΒΉ aβ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | all_goals
simp only [occursIn]
tauto | case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : v = aβΒΉ β¨ v = aβ
β’ occursIn v (eq_ aβΒΉ aβ)
case not_
v : VarName
aβ : Fo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_const_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_const_ aβΒΉ aβ)
case pred_var_
v : VarName
aβΒΉ : PredName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (pred_var_ aβΒΉ aβ)
case eq_
v aβΒΉ aβ : VarName
h1 : v = aβΒΉ β¨ v ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | simp only [isFreeIn] at h1 | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : isFreeIn v (def_ aβΒΉ aβ)
β’ occursIn v (def_ aβΒΉ aβ) | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (def_ aβΒΉ aβ) | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : isFreeIn v (def_ aβΒΉ aβ)
β’ occursIn v (def_ aβΒΉ aβ)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | simp only [occursIn] | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (def_ aβΒΉ aβ) | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ v β aβ | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ occursIn v (def_ aβΒΉ aβ)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Binders.lean | FOL.NV.isFreeIn_imp_occursIn | [481, 1] | [492, 10] | tauto | case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ v β aβ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case def_
v : VarName
aβΒΉ : DefName
aβ : List VarName
h1 : v β aβ
β’ v β aβ
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | induction F generalizing binders V | D : Type
I : Interpretation D
V V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
binders : Finset VarName
F : Formula
h1 : admitsAux Ο binders F
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =>
if ds.length = (... | case pred_const_
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
aβΒΉ : PredName
aβ : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ aβΒΉ aβ)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ :=... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
binders : Finset VarName
F : Formula
h1 : admitsAux Ο binders F
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case pred_const_ X xs =>
simp only [replace]
simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case eq_ x y =>
simp only [replace]
simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case true_ | false_ =>
simp only [replace]
simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =>
if ds... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case not_ phi phi_ih =>
simp only [admitsAux] at h1
simp only [replace]
simp only [Holds]
congr! 1
exact phi_ih V binders h1 h2 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case forall_ x phi phi_ih | exists_ x phi phi_ih =>
simp only [admitsAux] at h1
simp only [replace]
simp only [Holds]
first | apply forall_congr' | apply exists_congr
intro d
apply phi_ih (Function.updateITE V x d) (binders βͺ {x}) h1
intro v a1
simp only [Function.updateITE]
simp at a1
push_neg at a... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_const_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [admitsAux] at h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_var_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 :
Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2 β§
(β x β binders, Β¬(isFreeIn x (Ο X xs.length)... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (pred_var_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp at h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 :
Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2 β§
(β x β binders, Β¬(isFreeIn x (Ο X xs.length)... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1 :
Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2 β§
(β x β binder... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 :
Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | cases h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1 :
Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2 β§
(β x β binder... | case intro
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
leftβ : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
rightβ ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1 :
Var.All.Rec.admits (Function.updateListITE i... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | cases h1_right | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right : (β x ... | case intro
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
leftβ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | obtain s1 :=
Sub.Var.All.Rec.substitution_theorem D I V E (Function.updateListITE id (Ο X xs.length).fst xs)
(Ο X xs.length).snd h1_left | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Function.updateListITE_comp] at s1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp at s1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [s2] at s1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | clear s2 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [if_pos h1_right_right] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact s1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply Holds_coincide_Var | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : ... | case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListIT... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | intro v a1 | case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right... | case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upda... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | by_cases c1 : v β (Ο X xs.length).fst | case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upda... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply Function.updateListITE_mem_eq_len V V' v (Ο X xs.length).fst (List.map V xs) c1 | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | symm | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact h1_right_right | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | by_cases c2 : v β binders | case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | specialize h1_right_left v c2 a1 | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | contradiction | case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pos
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | specialize h2 v c2 | case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_righ... | case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : β x β binders, isFreeI... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h2 : β x β binders, V x = V' x
h1_left : Var.All.Rec.admits (Function.upd... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply Function.updateListITE_mem' | case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : β x β binders, isFreeI... | case neg.h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : β x β binders, isFr... | Please generate a tactic in lean4 to solve the state.
STATE:
case neg
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact h2 | case neg.h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length).1 xs) (Ο X xs.length).2
h1_right_left : β x β binders, isFr... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case neg.h1
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : PredName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1_left : Var.All.Rec.admits (Function.updateListITE id (Ο X xs.length... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (eq_ x y)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =>
if ds... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =>
if ds... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := fun X ds =>
if ds... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders false_
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [admitsAux] at h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
... | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ :=... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact phi_ih V binders h1 h2 | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ :=... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [admitsAux] at h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | cases h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | case intro
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | congr! 1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.pred_cons... | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Ho... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact phi_ih V binders h1_left h2 | case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_1.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact psi_ih V binders h1_right h2 | case a.h.e'_2.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h.e'_2.a
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
phi psi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [admitsAux] at h1 | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | first | apply forall_congr' | apply exists_congr | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | intro d | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply phi_ih (Function.updateITE V x d) (binders βͺ {x}) h1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | intro v a1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Function.updateITE] | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp at a1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | push_neg at a1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | cases a1 | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | case h.intro
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_... | Please generate a tactic in lean4 to solve the state.
STATE:
case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case h.intro a1_left a1_right =>
simp only [if_neg a1_right]
exact h2 v a1_left | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply forall_congr' | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | apply exists_congr | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | case h
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [if_neg a1_right] | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | exact h2 v a1_left | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
(Holds D
{ nonempty := β―, pred_const_ := I.p... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
x : VarName
phi : Formula
phi_ih :
β (V : VarAssignment D) (binders : Finset VarName),
admitsAux Ο binders phi β
(β x β binders, V x = V' x) β
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | cases E | D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_... | case nil
D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
E : Env
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | case nil =>
simp only [replace]
simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonem... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := ... | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := ... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonem... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [Holds] | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonempty := β―, pred_const_ := I.pred_const_,
pred_var_ := ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
β’ Holds D
{ nonem... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Sub/Pred/All/Rec/Sub.lean | FOL.NV.Sub.Pred.All.Rec.substitution_theorem_aux | [109, 1] | [238, 15] | simp only [replace] | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
hd : Definition
tl : List Definition
β’ Holds D
{ nonempty := β―, pred_const_ :=... | D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
hd : Definition
tl : List Definition
β’ Holds D
{ nonempty := β―, pred_const_ :=... | Please generate a tactic in lean4 to solve the state.
STATE:
D : Type
I : Interpretation D
V' : VarAssignment D
Ο : PredName β β β List VarName Γ Formula
X : DefName
xs : List VarName
V : VarAssignment D
binders : Finset VarName
h1 : admitsAux Ο binders (def_ X xs)
h2 : β x β binders, V x = V' x
hd : Definition
tl : Li... |
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