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.T_18_8
|
[1068, 1]
|
[1083, 37]
|
apply T_18_6
|
case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅ ((forall_ u P_u.not_).iff_ (forall_ v P_v.not_))
|
case a.h1
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅ ((forall_ u P_u.not_).iff_ (forall_ v P_v.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_18_8
|
[1068, 1]
|
[1083, 37]
|
exact similar_not P_u P_v u v h1
|
case a.h1
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T18_9
|
[1086, 1]
|
[1098, 13]
|
apply C_18_4 (exists_ u P_u) (exists_ v P_v) Q Q' Δ h2
|
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q'
|
case h2
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v))
case h3
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q'
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T18_9
|
[1086, 1]
|
[1098, 13]
|
exact T_18_8 P_u P_v u v h3
|
case h2
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h2
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T18_9
|
[1086, 1]
|
[1098, 13]
|
exact h1
|
case h3
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h3
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply IsDeduct.mp_ ((forall_ v P).imp_ P)
|
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v P).iff_ P)
|
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P))
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v P).iff_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply IsDeduct.mp_ (P.imp_ (forall_ v P))
|
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P))
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)))
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (P.imp_ (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
simp only [def_iff_]
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)))
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P)))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
simp only [def_and_]
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P)))))
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_
(((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
SC
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_
(((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_
(((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply IsDeduct.axiom_
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (P.imp_ (forall_ v P))
|
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom (P.imp_ (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (P.imp_ (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
exact IsAxiom.pred_3_ v P h1
|
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom (P.imp_ (forall_ v P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom (P.imp_ (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply IsDeduct.axiom_
|
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).imp_ P)
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v P).imp_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply IsAxiom.pred_2_ v v P P
|
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v P).imp_ P)
|
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastAdmits v v P
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastReplaceFree v v P = P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply fastAdmits_self
|
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastAdmits v v P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastAdmits v v P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_1
|
[1101, 1]
|
[1119, 33]
|
apply fastReplaceFree_self
|
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastReplaceFree v v P = P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastReplaceFree v v P = P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
apply IsDeduct.mp_ ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P)))
|
P : Formula
u v : VarName
⊢ IsProof ((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))
|
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))))
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ u (forall_ v P)).imp_ (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)).iff_ (forall_ v (forall_ u P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
apply IsDeduct.mp_ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P)))
|
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))))
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))))
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
simp only [def_iff_]
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))))
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).and_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
simp only [def_and_]
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).and_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))))))
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).not_).not_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).and_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
SC
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).not_).not_))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).not_).not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
apply T_17_10
|
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_2
|
[1122, 1]
|
[1135, 18]
|
apply T_17_10
|
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((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_19_3
|
[1138, 1]
|
[1149, 5]
|
simp only [def_exists_]
|
P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (exists_ v P).not_)
|
P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (forall_ v P.not_).not_.not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (exists_ v P).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_3
|
[1138, 1]
|
[1149, 5]
|
simp only [def_iff_]
|
P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (forall_ v P.not_).not_.not_)
|
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).and_ ((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (forall_ v P.not_).not_.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_3
|
[1138, 1]
|
[1149, 5]
|
simp only [def_and_]
|
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).and_ ((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)))
|
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).imp_
((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).and_ ((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_3
|
[1138, 1]
|
[1149, 5]
|
SC
|
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).imp_
((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)).not_).not_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).imp_
((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply deduction_theorem
|
P : Formula
u v : VarName
⊢ IsProof ((exists_ u (forall_ v P)).imp_ (forall_ v (exists_ u P)))
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {exists_ u (forall_ v P)}) (forall_ v (exists_ u P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
u v : VarName
⊢ IsProof ((exists_ u (forall_ v P)).imp_ (forall_ v (exists_ u P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {exists_ u (forall_ v P)}) (forall_ v (exists_ u P))
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (forall_ v (exists_ u P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {exists_ u (forall_ v P)}) (forall_ v (exists_ u P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply generalization
|
case h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (forall_ v (exists_ u P))
|
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u P)
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ 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 {exists_ u (forall_ v P)} (forall_ v (exists_ u P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply rule_C (forall_ v P) (exists_ u P) u {exists_ u (forall_ v P)}
|
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u P)
|
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u (forall_ v P))
case h1.h1.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (exists_ u P)
case h1.h1.h3
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn u H
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u (forall_ v P))
|
case h1.h1.h1.a
P : Formula
u v : VarName
⊢ exists_ u (forall_ v P) ∈ {exists_ u (forall_ v P)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h1.h1.a
P : Formula
u v : VarName
⊢ exists_ u (forall_ v P) ∈ {exists_ u (forall_ v P)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P : Formula
u v : VarName
⊢ exists_ u (forall_ v P) ∈ {exists_ u (forall_ v P)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply exists_intro P u u
|
case h1.h1.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (exists_ u P)
|
case h1.h1.h2.h1
P : Formula
u v : VarName
⊢ fastAdmits u u P
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (fastReplaceFree u u P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (exists_ u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply fastAdmits_self
|
case h1.h1.h2.h1
P : Formula
u v : VarName
⊢ fastAdmits u u P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h1
P : Formula
u v : VarName
⊢ fastAdmits u u P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [fastReplaceFree_self]
|
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (fastReplaceFree u u P)
|
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (fastReplaceFree u u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply specId v
|
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) P
|
case h1.h1.h2.h2.h1
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (forall_ v P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h2.h2.h1
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (forall_ v P)
|
case h1.h1.h2.h2.h1.a
P : Formula
u v : VarName
⊢ forall_ v P ∈ {exists_ u (forall_ v P)} ∪ {forall_ v P}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.h1
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h1.h2.h2.h1.a
P : Formula
u v : VarName
⊢ forall_ v P ∈ {exists_ u (forall_ v P)} ∪ {forall_ v P}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.h1.a
P : Formula
u v : VarName
⊢ forall_ v P ∈ {exists_ u (forall_ v P)} ∪ {forall_ v P}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h1.h3
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn u H
|
case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn u H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [def_exists_]
|
case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u (forall_ v P))
|
case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [isFreeIn]
|
case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P).not_).not_
|
case h1.h1.h3
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.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h1.h3
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.h3
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_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [def_exists_]
|
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u P)
|
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u P.not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [isFreeIn]
|
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u P.not_).not_
|
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬(¬True ∧ isFreeIn u P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u P.not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬(¬True ∧ isFreeIn u P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬(¬True ∧ isFreeIn u P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp
|
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn v H
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (exists_ u (forall_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [def_exists_]
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (exists_ u (forall_ v P))
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (forall_ u (forall_ v P).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (exists_ u (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 9]
|
simp only [isFreeIn]
|
case h1.h2
P : Formula
u v : VarName
⊢ ¬isFreeIn v (forall_ u (forall_ v P).not_).not_
|
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).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_4
|
[1152, 1]
|
[1183, 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_19_5
|
[1186, 1]
|
[1200, 24]
|
apply IsDeduct.mp_ ((forall_ v P).iff_ P)
|
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q))))
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).iff_ P)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))).imp_
(((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))))
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
simp only [def_iff_]
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))).imp_
(((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P)))).imp_
((((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((P.imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ P)))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))).imp_
(((forall_ v P).iff_ P).imp_ ((forall_ v (P.iff_ Q)).imp_ (P.iff_ (forall_ v Q)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
simp only [def_and_]
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P)))).imp_
((((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((P.imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ P)))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_).imp_
((((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_.imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((P.imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ P).not_).not_)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ (forall_ v P)))).imp_
((((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((P.imp_ (forall_ v Q)).and_ ((forall_ v Q).imp_ P)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
SC
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_).imp_
((((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_.imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((P.imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ P).not_).not_)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P).imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ (forall_ v P)).not_).not_).imp_
((((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_.imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((P.imp_ (forall_ v Q)).imp_ ((forall_ v Q).imp_ P).not_).not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
exact T_18_1 P Q v
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_5
|
[1186, 1]
|
[1200, 24]
|
exact T_19_1 P v h1
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).iff_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).iff_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q)))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v P).imp_ (exists_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply deduction_theorem
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v P).imp_ (exists_ v Q))
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)} ∪ {exists_ v P}) (exists_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v P).imp_ (exists_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)} ∪ {exists_ v P}) (exists_ v Q)
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)} ∪ {exists_ v P}) (exists_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply rule_C P (exists_ v Q) v {exists_ v P, forall_ v (P.iff_ Q)}
|
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v Q)
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v P)
case h1.h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (exists_ v Q)
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v P, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (exists_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v P)
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v P ∈ {exists_ v P, forall_ v (P.iff_ Q)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v P, forall_ v (P.iff_ Q)} (exists_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v P ∈ {exists_ v P, forall_ v (P.iff_ Q)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ exists_ v P ∈ {exists_ v P, forall_ v (P.iff_ Q)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply exists_intro Q v v
|
case h1.h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (exists_ v Q)
|
case h1.h1.h2.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (fastReplaceFree v v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (exists_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply fastAdmits_self
|
case h1.h1.h2.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h1
P Q : Formula
v : VarName
⊢ fastAdmits v v Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [fastReplaceFree_self]
|
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (fastReplaceFree v v Q)
|
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (fastReplaceFree v v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply IsDeduct.mp_ P
|
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) Q
|
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.imp_ Q)
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply IsDeduct.mp_ (P.iff_ Q)
|
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.imp_ Q)
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) ((P.iff_ Q).imp_ (P.imp_ Q))
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.iff_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [def_iff_]
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) ((P.iff_ Q).imp_ (P.imp_ Q))
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {P}) (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) ((P.iff_ Q).imp_ (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [def_and_]
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {P}) (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_} ∪ {P})
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {P}) (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
SC
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_} ∪ {P})
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_} ∪ {P})
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply specId v
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.iff_ Q)
|
case h1.h1.h2.h2.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (forall_ v (P.iff_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (P.iff_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h2.h2.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (forall_ v (P.iff_ Q))
|
case h1.h1.h2.h2.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) (forall_ v (P.iff_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h2.h2.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
apply IsDeduct.assume_
|
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) P
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ P ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ P ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2.h2.a.a
P Q : Formula
v : VarName
⊢ P ∈ {exists_ v P, forall_ v (P.iff_ Q)} ∪ {P}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [def_exists_]
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v P, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v P.not_).not_, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v P, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v P.not_).not_, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P.not_).not_ ∧ ¬isFreeIn v (forall_ v (P.iff_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {(forall_ v P.not_).not_, forall_ v (P.iff_ Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [isFreeIn]
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P.not_).not_ ∧ ¬isFreeIn v (forall_ v (P.iff_ Q))
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P.not_).not_ ∧ ¬isFreeIn v (forall_ v (P.iff_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h3
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [def_exists_]
|
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (exists_ v Q)
|
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q.not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (exists_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp only [isFreeIn]
|
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q.not_).not_
|
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q.not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_left
|
[1203, 1]
|
[1237, 9]
|
simp
|
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h4
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v Q).imp_ (exists_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v Q).imp_ (exists_ v P))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((exists_ v Q).imp_ (exists_ v P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v (P.iff_ Q)}) ((exists_ v Q).imp_ (exists_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply IsDeduct.mp_ (forall_ v (Q.iff_ P))
|
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((exists_ v Q).imp_ (exists_ v P))
|
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (Q.iff_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((exists_ v Q).imp_ (exists_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply proof_imp_deduct
|
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply T_19_6_left Q P v
|
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (Q.iff_ P)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply generalization
|
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (Q.iff_ P))
|
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (Q.iff_ P)
case h1.a.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v (P.iff_ Q)}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (Q.iff_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply IsDeduct.mp_ (P.iff_ Q)
|
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (Q.iff_ P)
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((P.iff_ Q).imp_ (Q.iff_ P))
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (P.iff_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (Q.iff_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp only [def_iff_]
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((P.iff_ Q).imp_ (Q.iff_ P))
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ ((Q.imp_ P).and_ (P.imp_ Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} ((P.iff_ Q).imp_ (Q.iff_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp only [def_and_]
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ ((Q.imp_ P).and_ (P.imp_ Q)))
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ ((Q.imp_ P).imp_ (P.imp_ Q).not_).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ ((Q.imp_ P).and_ (P.imp_ Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
SC
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ ((Q.imp_ P).imp_ (P.imp_ Q).not_).not_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ ((Q.imp_ P).imp_ (P.imp_ Q).not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply specId v
|
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (P.iff_ Q)
|
case h1.a.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (P.iff_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (P.iff_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
apply IsDeduct.assume_
|
case h1.a.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (P.iff_ Q))
|
case h1.a.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {forall_ v (P.iff_ Q)}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v (P.iff_ Q)} (forall_ v (P.iff_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp
|
case h1.a.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {forall_ v (P.iff_ Q)}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v (P.iff_ Q) ∈ {forall_ v (P.iff_ Q)}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp
|
case h1.a.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v (P.iff_ Q)}, ¬isFreeIn v H
|
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.iff_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v (P.iff_ Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp only [isFreeIn]
|
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.iff_ Q))
|
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v (P.iff_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6_right
|
[1240, 1]
|
[1262, 11]
|
simp
|
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ (isFreeIn v P ∨ isFreeIn v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q)))
|
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).iff_ (exists_ v Q)))
|
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q))).imp_
((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).iff_ (exists_ v Q))))
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).iff_ (exists_ v Q)))
TACTIC:
|
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