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/Margaris/Fol.lean
|
FOL.NV.isProofAltImpIsDeduct
|
[402, 1]
|
[446, 10]
|
sorry
|
case def_exists_
F : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsDeduct ∅ ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case def_exists_
F : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsDeduct ∅ ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
induction h1
|
F : Formula
h1 : IsDeduct ∅ F
⊢ IsProofAlt F
|
case axiom_
F phi✝ : Formula
a✝ : IsAxiom phi✝
⊢ IsProofAlt phi✝
case assume_
F phi✝ : Formula
a✝ : phi✝ ∈ ∅
⊢ IsProofAlt phi✝
case mp_
F phi✝ psi✝ : Formula
a✝¹ : IsDeduct ∅ (phi✝.imp_ psi✝)
a✝ : IsDeduct ∅ phi✝
a_ih✝¹ : IsProofAlt (phi✝.imp_ psi✝)
a_ih✝ : IsProofAlt phi✝
⊢ IsProofAlt psi✝
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
h1 : IsDeduct ∅ F
⊢ IsProofAlt F
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case axiom_ h1_phi h1_1 =>
induction h1_1
case prop_true_ =>
apply IsProofAlt.prop_true_
case prop_1_ h1_1_phi h1_1_psi =>
apply IsProofAlt.prop_1_
case prop_2_ h1_1_phi h1_1_psi h1_1_chi =>
apply IsProofAlt.prop_2_
case prop_3_ h1_1_phi h1_1_psi =>
apply IsProofAlt.prop_3_
case pred_1_ h1_1_v h1_1_phi h1_1_psi =>
apply IsProofAlt.pred_1_
case pred_2_ h1_1_v h1_1_t h1_1_phi h1_1_1 h1_1_ih_1 h1_1_ih_2 =>
apply IsProofAlt.pred_2_ h1_1_v h1_1_t h1_1_phi h1_1_1 h1_1_ih_1 h1_1_ih_2
case pred_3_ h1_1_v h1_1_phi h1_1_1 =>
apply IsProofAlt.pred_3_
exact h1_1_1
case eq_1_ h1_1 =>
apply IsProofAlt.eq_1_
case eq_2_pred_const_ h1_1_name h1_1_n h1_1_xs h1_1_ys =>
apply IsProofAlt.eq_2_pred_const_
case eq_2_eq_ h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 =>
apply IsProofAlt.eq_2_eq_
case gen_ h1_1_v h1_1_phi h1_1_1 h1_1_ih =>
apply IsProofAlt.gen_
exact h1_1_ih
all_goals
sorry
|
F h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsProofAlt h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsProofAlt h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case assume_ h1_phi h1_1 =>
simp at h1_1
|
F h1_phi : Formula
h1_1 : h1_phi ∈ ∅
⊢ IsProofAlt h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : h1_phi ∈ ∅
⊢ IsProofAlt h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case mp_ h1_phi h1_psi h1_1 h1_2 h1_ih_1 h1_ih_2 =>
exact IsProofAlt.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F h1_phi h1_psi : Formula
h1_1 : IsDeduct ∅ (h1_phi.imp_ h1_psi)
h1_2 : IsDeduct ∅ h1_phi
h1_ih_1 : IsProofAlt (h1_phi.imp_ h1_psi)
h1_ih_2 : IsProofAlt h1_phi
⊢ IsProofAlt h1_psi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_psi : Formula
h1_1 : IsDeduct ∅ (h1_phi.imp_ h1_psi)
h1_2 : IsDeduct ∅ h1_phi
h1_ih_1 : IsProofAlt (h1_phi.imp_ h1_psi)
h1_ih_2 : IsProofAlt h1_phi
⊢ IsProofAlt h1_psi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
induction h1_1
|
F h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsProofAlt h1_phi
|
case prop_true_
F h1_phi : Formula
⊢ IsProofAlt true_
case prop_1_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt (phi✝.imp_ (psi✝.imp_ phi✝))
case prop_2_
F h1_phi phi✝ psi✝ chi✝ : Formula
⊢ IsProofAlt ((phi✝.imp_ (psi✝.imp_ chi✝)).imp_ ((phi✝.imp_ psi✝).imp_ (phi✝.imp_ chi✝)))
case prop_3_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.not_.imp_ psi✝.not_).imp_ (psi✝.imp_ phi✝))
case pred_1_
F h1_phi : Formula
v✝ : VarName
phi✝ psi✝ : Formula
⊢ IsProofAlt ((forall_ v✝ (phi✝.imp_ psi✝)).imp_ ((forall_ v✝ phi✝).imp_ (forall_ v✝ psi✝)))
case pred_2_
F h1_phi : Formula
v✝ t✝ : VarName
phi✝ phi'✝ : Formula
a✝¹ : fastAdmits v✝ t✝ phi✝
a✝ : fastReplaceFree v✝ t✝ phi✝ = phi'✝
⊢ IsProofAlt ((forall_ v✝ phi✝).imp_ phi'✝)
case pred_3_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
a✝ : ¬isFreeIn v✝ phi✝
⊢ IsProofAlt (phi✝.imp_ (forall_ v✝ phi✝))
case eq_1_
F h1_phi : Formula
v✝ : VarName
⊢ IsProofAlt (forall_ v✝ (eq_ v✝ v✝))
case eq_2_pred_const_
F h1_phi : Formula
name✝ : PredName
n✝ : ℕ
xs✝ ys✝ : Fin n✝ → VarName
⊢ IsProofAlt
(Forall_ (List.ofFn xs✝)
(Forall_ (List.ofFn ys✝)
((And_ (List.ofFn fun i => eq_ (xs✝ i) (ys✝ i))).imp_
((pred_const_ name✝ (List.ofFn xs✝)).iff_ (pred_const_ name✝ (List.ofFn ys✝))))))
case eq_2_eq_
F h1_phi : Formula
x_0✝ x_1✝ y_0✝ y_1✝ : VarName
⊢ IsProofAlt
(forall_ x_0✝
(forall_ x_1✝
(forall_ y_0✝
(forall_ y_1✝ (((eq_ x_0✝ y_0✝).and_ (eq_ x_1✝ y_1✝)).imp_ ((eq_ x_0✝ x_1✝).iff_ (eq_ y_0✝ y_1✝)))))))
case gen_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
a✝ : IsAxiom phi✝
a_ih✝ : IsProofAlt phi✝
⊢ IsProofAlt (forall_ v✝ phi✝)
case def_false_
F h1_phi : Formula
⊢ IsProofAlt (false_.iff_ true_.not_)
case def_and_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.and_ psi✝).iff_ (phi✝.imp_ psi✝.not_).not_)
case def_or_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.or_ psi✝).iff_ (phi✝.not_.imp_ psi✝))
case def_iff_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt
(((phi✝.iff_ psi✝).imp_ ((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_).imp_
(((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_.imp_ (phi✝.iff_ psi✝)).not_).not_
case def_exists_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsProofAlt ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsProofAlt h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case prop_true_ =>
apply IsProofAlt.prop_true_
|
F h1_phi : Formula
⊢ IsProofAlt true_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
⊢ IsProofAlt true_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case prop_1_ h1_1_phi h1_1_psi =>
apply IsProofAlt.prop_1_
|
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt (h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt (h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case prop_2_ h1_1_phi h1_1_psi h1_1_chi =>
apply IsProofAlt.prop_2_
|
F h1_phi h1_1_phi h1_1_psi h1_1_chi : Formula
⊢ IsProofAlt ((h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_chi)).imp_ ((h1_1_phi.imp_ h1_1_psi).imp_ (h1_1_phi.imp_ h1_1_chi)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi h1_1_chi : Formula
⊢ IsProofAlt ((h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_chi)).imp_ ((h1_1_phi.imp_ h1_1_psi).imp_ (h1_1_phi.imp_ h1_1_chi)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case prop_3_ h1_1_phi h1_1_psi =>
apply IsProofAlt.prop_3_
|
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((h1_1_phi.not_.imp_ h1_1_psi.not_).imp_ (h1_1_psi.imp_ h1_1_phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((h1_1_phi.not_.imp_ h1_1_psi.not_).imp_ (h1_1_psi.imp_ h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case pred_1_ h1_1_v h1_1_phi h1_1_psi =>
apply IsProofAlt.pred_1_
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((forall_ h1_1_v (h1_1_phi.imp_ h1_1_psi)).imp_ ((forall_ h1_1_v h1_1_phi).imp_ (forall_ h1_1_v h1_1_psi)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((forall_ h1_1_v (h1_1_phi.imp_ h1_1_psi)).imp_ ((forall_ h1_1_v h1_1_phi).imp_ (forall_ h1_1_v h1_1_psi)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case pred_2_ h1_1_v h1_1_t h1_1_phi h1_1_1 h1_1_ih_1 h1_1_ih_2 =>
apply IsProofAlt.pred_2_ h1_1_v h1_1_t h1_1_phi h1_1_1 h1_1_ih_1 h1_1_ih_2
|
F h1_phi : Formula
h1_1_v h1_1_t : VarName
h1_1_phi h1_1_1 : Formula
h1_1_ih_1 : fastAdmits h1_1_v h1_1_t h1_1_phi
h1_1_ih_2 : fastReplaceFree h1_1_v h1_1_t h1_1_phi = h1_1_1
⊢ IsProofAlt ((forall_ h1_1_v h1_1_phi).imp_ h1_1_1)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v h1_1_t : VarName
h1_1_phi h1_1_1 : Formula
h1_1_ih_1 : fastAdmits h1_1_v h1_1_t h1_1_phi
h1_1_ih_2 : fastReplaceFree h1_1_v h1_1_t h1_1_phi = h1_1_1
⊢ IsProofAlt ((forall_ h1_1_v h1_1_phi).imp_ h1_1_1)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case pred_3_ h1_1_v h1_1_phi h1_1_1 =>
apply IsProofAlt.pred_3_
exact h1_1_1
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ IsProofAlt (h1_1_phi.imp_ (forall_ h1_1_v h1_1_phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ IsProofAlt (h1_1_phi.imp_ (forall_ h1_1_v h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case eq_1_ h1_1 =>
apply IsProofAlt.eq_1_
|
F h1_phi : Formula
h1_1 : VarName
⊢ IsProofAlt (forall_ h1_1 (eq_ h1_1 h1_1))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : VarName
⊢ IsProofAlt (forall_ h1_1 (eq_ h1_1 h1_1))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case eq_2_pred_const_ h1_1_name h1_1_n h1_1_xs h1_1_ys =>
apply IsProofAlt.eq_2_pred_const_
|
F h1_phi : Formula
h1_1_name : PredName
h1_1_n : ℕ
h1_1_xs h1_1_ys : Fin h1_1_n → VarName
⊢ IsProofAlt
(Forall_ (List.ofFn h1_1_xs)
(Forall_ (List.ofFn h1_1_ys)
((And_ (List.ofFn fun i => eq_ (h1_1_xs i) (h1_1_ys i))).imp_
((pred_const_ h1_1_name (List.ofFn h1_1_xs)).iff_ (pred_const_ h1_1_name (List.ofFn h1_1_ys))))))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_name : PredName
h1_1_n : ℕ
h1_1_xs h1_1_ys : Fin h1_1_n → VarName
⊢ IsProofAlt
(Forall_ (List.ofFn h1_1_xs)
(Forall_ (List.ofFn h1_1_ys)
((And_ (List.ofFn fun i => eq_ (h1_1_xs i) (h1_1_ys i))).imp_
((pred_const_ h1_1_name (List.ofFn h1_1_xs)).iff_ (pred_const_ h1_1_name (List.ofFn h1_1_ys))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case eq_2_eq_ h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 =>
apply IsProofAlt.eq_2_eq_
|
F h1_phi : Formula
h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 : VarName
⊢ IsProofAlt
(forall_ h1_1_x_0
(forall_ h1_1_y_0
(forall_ h1_1_x_1
(forall_ h1_1_y_1
(((eq_ h1_1_x_0 h1_1_x_1).and_ (eq_ h1_1_y_0 h1_1_y_1)).imp_
((eq_ h1_1_x_0 h1_1_y_0).iff_ (eq_ h1_1_x_1 h1_1_y_1)))))))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 : VarName
⊢ IsProofAlt
(forall_ h1_1_x_0
(forall_ h1_1_y_0
(forall_ h1_1_x_1
(forall_ h1_1_y_1
(((eq_ h1_1_x_0 h1_1_x_1).and_ (eq_ h1_1_y_0 h1_1_y_1)).imp_
((eq_ h1_1_x_0 h1_1_y_0).iff_ (eq_ h1_1_x_1 h1_1_y_1)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
case gen_ h1_1_v h1_1_phi h1_1_1 h1_1_ih =>
apply IsProofAlt.gen_
exact h1_1_ih
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt (forall_ h1_1_v h1_1_phi)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt (forall_ h1_1_v h1_1_phi)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
all_goals
sorry
|
case def_false_
F h1_phi : Formula
⊢ IsProofAlt (false_.iff_ true_.not_)
case def_and_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.and_ psi✝).iff_ (phi✝.imp_ psi✝.not_).not_)
case def_or_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.or_ psi✝).iff_ (phi✝.not_.imp_ psi✝))
case def_iff_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt
(((phi✝.iff_ psi✝).imp_ ((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_).imp_
(((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_.imp_ (phi✝.iff_ psi✝)).not_).not_
case def_exists_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsProofAlt ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case def_false_
F h1_phi : Formula
⊢ IsProofAlt (false_.iff_ true_.not_)
case def_and_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.and_ psi✝).iff_ (phi✝.imp_ psi✝.not_).not_)
case def_or_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt ((phi✝.or_ psi✝).iff_ (phi✝.not_.imp_ psi✝))
case def_iff_
F h1_phi phi✝ psi✝ : Formula
⊢ IsProofAlt
(((phi✝.iff_ psi✝).imp_ ((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_).imp_
(((phi✝.imp_ psi✝).imp_ (psi✝.imp_ phi✝).not_).not_.imp_ (phi✝.iff_ psi✝)).not_).not_
case def_exists_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsProofAlt ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.prop_true_
|
F h1_phi : Formula
⊢ IsProofAlt true_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
⊢ IsProofAlt true_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.prop_1_
|
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt (h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt (h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.prop_2_
|
F h1_phi h1_1_phi h1_1_psi h1_1_chi : Formula
⊢ IsProofAlt ((h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_chi)).imp_ ((h1_1_phi.imp_ h1_1_psi).imp_ (h1_1_phi.imp_ h1_1_chi)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi h1_1_chi : Formula
⊢ IsProofAlt ((h1_1_phi.imp_ (h1_1_psi.imp_ h1_1_chi)).imp_ ((h1_1_phi.imp_ h1_1_psi).imp_ (h1_1_phi.imp_ h1_1_chi)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.prop_3_
|
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((h1_1_phi.not_.imp_ h1_1_psi.not_).imp_ (h1_1_psi.imp_ h1_1_phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((h1_1_phi.not_.imp_ h1_1_psi.not_).imp_ (h1_1_psi.imp_ h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.pred_1_
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((forall_ h1_1_v (h1_1_phi.imp_ h1_1_psi)).imp_ ((forall_ h1_1_v h1_1_phi).imp_ (forall_ h1_1_v h1_1_psi)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi h1_1_psi : Formula
⊢ IsProofAlt ((forall_ h1_1_v (h1_1_phi.imp_ h1_1_psi)).imp_ ((forall_ h1_1_v h1_1_phi).imp_ (forall_ h1_1_v h1_1_psi)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.pred_2_ h1_1_v h1_1_t h1_1_phi h1_1_1 h1_1_ih_1 h1_1_ih_2
|
F h1_phi : Formula
h1_1_v h1_1_t : VarName
h1_1_phi h1_1_1 : Formula
h1_1_ih_1 : fastAdmits h1_1_v h1_1_t h1_1_phi
h1_1_ih_2 : fastReplaceFree h1_1_v h1_1_t h1_1_phi = h1_1_1
⊢ IsProofAlt ((forall_ h1_1_v h1_1_phi).imp_ h1_1_1)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v h1_1_t : VarName
h1_1_phi h1_1_1 : Formula
h1_1_ih_1 : fastAdmits h1_1_v h1_1_t h1_1_phi
h1_1_ih_2 : fastReplaceFree h1_1_v h1_1_t h1_1_phi = h1_1_1
⊢ IsProofAlt ((forall_ h1_1_v h1_1_phi).imp_ h1_1_1)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.pred_3_
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ IsProofAlt (h1_1_phi.imp_ (forall_ h1_1_v h1_1_phi))
|
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ ¬isFreeIn h1_1_v h1_1_phi
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ IsProofAlt (h1_1_phi.imp_ (forall_ h1_1_v h1_1_phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
exact h1_1_1
|
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ ¬isFreeIn h1_1_v h1_1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : ¬isFreeIn h1_1_v h1_1_phi
⊢ ¬isFreeIn h1_1_v h1_1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.eq_1_
|
F h1_phi : Formula
h1_1 : VarName
⊢ IsProofAlt (forall_ h1_1 (eq_ h1_1 h1_1))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : VarName
⊢ IsProofAlt (forall_ h1_1 (eq_ h1_1 h1_1))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.eq_2_pred_const_
|
F h1_phi : Formula
h1_1_name : PredName
h1_1_n : ℕ
h1_1_xs h1_1_ys : Fin h1_1_n → VarName
⊢ IsProofAlt
(Forall_ (List.ofFn h1_1_xs)
(Forall_ (List.ofFn h1_1_ys)
((And_ (List.ofFn fun i => eq_ (h1_1_xs i) (h1_1_ys i))).imp_
((pred_const_ h1_1_name (List.ofFn h1_1_xs)).iff_ (pred_const_ h1_1_name (List.ofFn h1_1_ys))))))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_name : PredName
h1_1_n : ℕ
h1_1_xs h1_1_ys : Fin h1_1_n → VarName
⊢ IsProofAlt
(Forall_ (List.ofFn h1_1_xs)
(Forall_ (List.ofFn h1_1_ys)
((And_ (List.ofFn fun i => eq_ (h1_1_xs i) (h1_1_ys i))).imp_
((pred_const_ h1_1_name (List.ofFn h1_1_xs)).iff_ (pred_const_ h1_1_name (List.ofFn h1_1_ys))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.eq_2_eq_
|
F h1_phi : Formula
h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 : VarName
⊢ IsProofAlt
(forall_ h1_1_x_0
(forall_ h1_1_y_0
(forall_ h1_1_x_1
(forall_ h1_1_y_1
(((eq_ h1_1_x_0 h1_1_x_1).and_ (eq_ h1_1_y_0 h1_1_y_1)).imp_
((eq_ h1_1_x_0 h1_1_y_0).iff_ (eq_ h1_1_x_1 h1_1_y_1)))))))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_x_0 h1_1_y_0 h1_1_x_1 h1_1_y_1 : VarName
⊢ IsProofAlt
(forall_ h1_1_x_0
(forall_ h1_1_y_0
(forall_ h1_1_x_1
(forall_ h1_1_y_1
(((eq_ h1_1_x_0 h1_1_x_1).and_ (eq_ h1_1_y_0 h1_1_y_1)).imp_
((eq_ h1_1_x_0 h1_1_y_0).iff_ (eq_ h1_1_x_1 h1_1_y_1)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
apply IsProofAlt.gen_
|
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt (forall_ h1_1_v h1_1_phi)
|
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt h1_1_phi
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt (forall_ h1_1_v h1_1_phi)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
exact h1_1_ih
|
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt h1_1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
F h1_phi : Formula
h1_1_v : VarName
h1_1_phi : Formula
h1_1_1 : IsAxiom h1_1_phi
h1_1_ih : IsProofAlt h1_1_phi
⊢ IsProofAlt h1_1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
sorry
|
case def_exists_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsProofAlt ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case def_exists_
F h1_phi : Formula
v✝ : VarName
phi✝ : Formula
⊢ IsProofAlt ((exists_ v✝ phi✝).iff_ (forall_ v✝ phi✝.not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
simp at h1_1
|
F h1_phi : Formula
h1_1 : h1_phi ∈ ∅
⊢ IsProofAlt h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi : Formula
h1_1 : h1_phi ∈ ∅
⊢ IsProofAlt h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.isDeductImpIsProofAlt
|
[449, 1]
|
[486, 55]
|
exact IsProofAlt.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F h1_phi h1_psi : Formula
h1_1 : IsDeduct ∅ (h1_phi.imp_ h1_psi)
h1_2 : IsDeduct ∅ h1_phi
h1_ih_1 : IsProofAlt (h1_phi.imp_ h1_psi)
h1_ih_2 : IsProofAlt h1_phi
⊢ IsProofAlt h1_psi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F h1_phi h1_psi : Formula
h1_1 : IsDeduct ∅ (h1_phi.imp_ h1_psi)
h1_2 : IsDeduct ∅ h1_phi
h1_ih_1 : IsProofAlt (h1_phi.imp_ h1_psi)
h1_ih_2 : IsProofAlt h1_phi
⊢ IsProofAlt h1_psi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply deduction_theorem
|
P : Formula
u v : VarName
⊢ IsProof ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P)))
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {forall_ u (forall_ v P)}) (forall_ v (forall_ u P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
u v : VarName
⊢ IsProof ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {forall_ u (forall_ v P)}) (forall_ v (forall_ u P))
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v (forall_ u P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {forall_ u (forall_ v P)}) (forall_ v (forall_ u P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply generalization
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v (forall_ u P))
|
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u P)
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v (forall_ u P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply generalization
|
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u P)
|
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} P
case h1.h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn u H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply specId v P
|
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} P
|
case h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply specId u (forall_ v P)
|
case h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v P)
|
case h1.h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u (forall_ v P))
|
case h1.h1.h1.h1.h1.a
P : Formula
u v : VarName
⊢ forall_ u (forall_ v P) ∈ {forall_ u (forall_ v P)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {forall_ u (forall_ v P)} (forall_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1.h1.h1.h1.h1.a
P : Formula
u v : VarName
⊢ forall_ u (forall_ v P) ∈ {forall_ u (forall_ v P)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.h1.a
P : Formula
u v : VarName
⊢ forall_ u (forall_ v P) ∈ {forall_ u (forall_ v P)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn u H
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn u H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp only [isFreeIn]
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P))
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬(¬True ∧ ¬u = v ∧ isFreeIn u P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬(¬True ∧ ¬u = v ∧ isFreeIn u P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P : Formula
u v : VarName
⊢ ¬(¬True ∧ ¬u = v ∧ isFreeIn u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn v H
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (forall_ u (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {forall_ u (forall_ v P)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp only [isFreeIn]
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (forall_ u (forall_ v P))
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬(¬v = u ∧ ¬True ∧ isFreeIn v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (forall_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_10
|
[489, 1]
|
[507, 9]
|
simp
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬(¬v = u ∧ ¬True ∧ isFreeIn v P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P : Formula
u v : VarName
⊢ ¬(¬v = u ∧ ¬True ∧ isFreeIn v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct (∅ ∪ {forall_ v (P.imp_ Q)}) ((exists_ v P).imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct (∅ ∪ {forall_ v (P.imp_ Q)}) ((exists_ v P).imp_ Q)
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((exists_ v P).imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct (∅ ∪ {forall_ v (P.imp_ Q)}) ((exists_ v P).imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp only [def_exists_]
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((exists_ v P).imp_ Q)
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v P.not_).not_.imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((exists_ v P).imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.mp_ (Q.not_.imp_ (forall_ v Q.not_))
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v P.not_).not_.imp_ Q)
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q))
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ (forall_ v Q.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v P.not_).not_.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.mp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_))
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q))
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)}
(((forall_ v Q.not_).imp_ (forall_ v P.not_)).imp_
((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q)))
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v Q.not_).imp_ (forall_ v P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
SC
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)}
(((forall_ v Q.not_).imp_ (forall_ v P.not_)).imp_
((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)}
(((forall_ v Q.not_).imp_ (forall_ v P.not_)).imp_
((Q.not_.imp_ (forall_ v Q.not_)).imp_ ((forall_ v P.not_).not_.imp_ Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.mp_ (forall_ v (Q.not_.imp_ P.not_))
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v Q.not_).imp_ (forall_ v P.not_))
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (Q.not_.imp_ P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v Q.not_).imp_ (forall_ v P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.axiom_
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
|
case h1.a.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsAxiom.pred_1_
|
case h1.a.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom ((forall_ v (Q.not_.imp_ P.not_)).imp_ ((forall_ v Q.not_).imp_ (forall_ v P.not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply generalization
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (Q.not_.imp_ P.not_))
|
case h1.a.a.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ P.not_)
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ∀ H ∈ {forall_ v (P.imp_ Q)}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (Q.not_.imp_ P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.mp_ (P.imp_ Q)
|
case h1.a.a.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ P.not_)
|
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (P.imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ P.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply proof_imp_deduct
|
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
|
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsProof ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply T_14_7
|
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsProof ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsProof ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply specId v (P.imp_ Q)
|
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (P.imp_ Q)
|
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.assume_
|
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (P.imp_ Q))
|
case h1.a.a.a.h1.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ forall_ v (P.imp_ Q) ∈ {forall_ v (P.imp_ Q)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1.a.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (forall_ v (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp
|
case h1.a.a.a.h1.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ forall_ v (P.imp_ Q) ∈ {forall_ v (P.imp_ Q)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1.a.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ forall_ v (P.imp_ Q) ∈ {forall_ v (P.imp_ Q)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp
|
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ∀ H ∈ {forall_ v (P.imp_ Q)}, ¬isFreeIn v H
|
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ∀ H ∈ {forall_ v (P.imp_ Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp only [isFreeIn]
|
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q))
|
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v (forall_ v (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp
|
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsDeduct.axiom_
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ (forall_ v Q.not_))
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom (Q.not_.imp_ (forall_ v Q.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsDeduct {forall_ v (P.imp_ Q)} (Q.not_.imp_ (forall_ v Q.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
apply IsAxiom.pred_3_
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom (Q.not_.imp_ (forall_ v Q.not_))
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q.not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ IsAxiom (Q.not_.imp_ (forall_ v Q.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
simp only [isFreeIn]
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q.not_
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q.not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_11
|
[510, 1]
|
[539, 13]
|
exact h1
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v Q
⊢ ¬isFreeIn v Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
apply IsDeduct.mp_ (exists_ v P)
|
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ Q
|
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((exists_ v P).imp_ Q)
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (exists_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
apply IsDeduct.mp_ (forall_ v (P.imp_ Q))
|
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((exists_ v P).imp_ Q)
|
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (forall_ v (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((exists_ v P).imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
apply proof_imp_deduct
|
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
|
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
exact T_17_11 P Q v h4
|
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ ((exists_ v P).imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
apply generalization
|
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (forall_ v (P.imp_ Q))
|
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (P.imp_ Q)
case a.a.h2
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ ∀ H ∈ Δ, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (forall_ v (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
apply deduction_theorem
|
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (P.imp_ Q)
|
case a.a.h1.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct (Δ ∪ {P}) Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
exact h2
|
case a.a.h1.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct (Δ ∪ {P}) Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h1.h1
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct (Δ ∪ {P}) Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
exact h3
|
case a.a.h2
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ ∀ H ∈ Δ, ¬isFreeIn v H
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.h2
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ ∀ H ∈ Δ, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_17_12
|
[543, 1]
|
[561, 13]
|
exact h1
|
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (exists_ v P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {P}) Q
h3 : ∀ H ∈ Δ, ¬isFreeIn v H
h4 : ¬isFreeIn v Q
⊢ IsDeduct Δ (exists_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
refine' rule_C (fastReplaceFree v t P) Q t Δ _ h2 h5 _
|
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ IsDeduct Δ Q
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
case refine'_2
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ ¬isFreeIn t Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ IsDeduct Δ Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp only [def_exists_] at h1
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h1 : IsDeduct Δ (exists_ v P)
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp only [def_exists_]
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ t (fastReplaceFree v t P).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (exists_ t (fastReplaceFree v t P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply IsDeduct.mp_ (forall_ v P.not_).not_
|
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ t (fastReplaceFree v t P).not_).not_
|
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_)
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ v P.not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ (forall_ t (fastReplaceFree v t P).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply IsDeduct.mp_ ((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_))
|
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_)
|
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ
(((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_)).imp_
((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_))
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
SC
|
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ
(((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_)).imp_
((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ
(((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_)).imp_
((forall_ v P.not_).not_.imp_ (forall_ t (fastReplaceFree v t P).not_).not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply deduction_theorem
|
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_))
|
case refine'_1.a.a.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ v P.not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct Δ ((forall_ t (fastReplaceFree v t P.not_)).imp_ (forall_ v P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply univIntro P.not_ v t _ h3
|
case refine'_1.a.a.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ v P.not_)
|
case refine'_1.a.a.h1.h2
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (fastReplaceFree v t P.not_)
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ∀ H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}, ¬isFreeIn t H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ v P.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply specId t
|
case refine'_1.a.a.h1.h2
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (fastReplaceFree v t P.not_)
|
case refine'_1.a.a.h1.h2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ t (fastReplaceFree v t P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h2
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (fastReplaceFree v t P.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
apply IsDeduct.assume_
|
case refine'_1.a.a.h1.h2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ t (fastReplaceFree v t P.not_))
|
case refine'_1.a.a.h1.h2.h1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ forall_ t (fastReplaceFree v t P.not_) ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h2.h1
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ IsDeduct (Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}) (forall_ t (fastReplaceFree v t P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp
|
case refine'_1.a.a.h1.h2.h1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ forall_ t (fastReplaceFree v t P.not_) ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h2.h1.a
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ forall_ t (fastReplaceFree v t P.not_) ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
intro H a1
|
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ∀ H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}, ¬isFreeIn t H
|
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
⊢ ¬isFreeIn t H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ∀ H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}, ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp at a1
|
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
⊢ ¬isFreeIn t H
|
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H = forall_ t (fastReplaceFree v t P.not_) ∨ H ∈ Δ
⊢ ¬isFreeIn t H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H ∈ Δ ∪ {forall_ t (fastReplaceFree v t P.not_)}
⊢ ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
cases a1
|
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H = forall_ t (fastReplaceFree v t P.not_) ∨ H ∈ Δ
⊢ ¬isFreeIn t H
|
case refine'_1.a.a.h1.h3.inl
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
h✝ : H = forall_ t (fastReplaceFree v t P.not_)
⊢ ¬isFreeIn t H
case refine'_1.a.a.h1.h3.inr
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
h✝ : H ∈ Δ
⊢ ¬isFreeIn t H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case refine'_1.a.a.h1.h3
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
a1 : H = forall_ t (fastReplaceFree v t P.not_) ∨ H ∈ Δ
⊢ ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
case _ c1 =>
subst c1
simp only [isFreeIn]
simp
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H = forall_ t (fastReplaceFree v t P.not_)
⊢ ¬isFreeIn t H
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H = forall_ t (fastReplaceFree v t P.not_)
⊢ ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
case _ c1 =>
exact h5 H c1
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H ∈ Δ
⊢ ¬isFreeIn t H
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H ∈ Δ
⊢ ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
subst c1
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H = forall_ t (fastReplaceFree v t P.not_)
⊢ ¬isFreeIn t H
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬isFreeIn t (forall_ t (fastReplaceFree v t P.not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H = forall_ t (fastReplaceFree v t P.not_)
⊢ ¬isFreeIn t H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp only [isFreeIn]
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬isFreeIn t (forall_ t (fastReplaceFree v t P.not_))
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬(¬True ∧ isFreeIn t (fastReplaceFree v t P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬isFreeIn t (forall_ t (fastReplaceFree v t P.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
simp
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬(¬True ∧ isFreeIn t (fastReplaceFree v t P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
⊢ ¬(¬True ∧ isFreeIn t (fastReplaceFree v t P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.existsElim
|
[567, 1]
|
[603, 17]
|
exact h5 H c1
|
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H ∈ Δ
⊢ ¬isFreeIn t H
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v t : VarName
Δ : Set Formula
h2 : IsDeduct (Δ ∪ {fastReplaceFree v t P}) Q
h3 : ¬occursIn t P
h4 : ¬occursIn t Q
h5 : ∀ H ∈ Δ, ¬isFreeIn t H
h1 : IsDeduct Δ (forall_ v P.not_).not_
H : Formula
c1 : H ∈ Δ
⊢ ¬isFreeIn t H
TACTIC:
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.