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_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:
|
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 Q).imp_ (exists_ v P)))
|
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.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P))).imp_
(((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.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
simp only [def_exists_]
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P))).imp_
(((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.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.iff_ (forall_ v Q.not_).not_))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P))).imp_
(((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)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
simp only [def_iff_]
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.iff_ (forall_ v Q.not_).not_))))
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).and_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P.not_).not_.iff_ (forall_ v Q.not_).not_))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
simp only [def_and_]
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).and_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)))))
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_).not_).not_)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).and_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
SC
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_).not_).not_)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_)).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_)).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((forall_ v P.not_).not_.imp_ (forall_ v Q.not_).not_).imp_
((forall_ v Q.not_).not_.imp_ (forall_ v P.not_).not_).not_).not_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_6
|
[1265, 1]
|
[1280, 22]
|
apply T_19_6_right
|
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((exists_ v Q).imp_ (exists_ v P)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((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
|
[1265, 1]
|
[1280, 22]
|
apply T_19_6_left
|
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((exists_ v P).imp_ (exists_ v Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((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_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply C_18_4 (forall_ v P) P ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
case h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v P).iff_ P)
case h3
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsReplOfFormulaInFormula.imp_
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v (P.imp_ Q)) (forall_ v (P.imp_ Q))
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v P).imp_ (forall_ v Q)) (P.imp_ (forall_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsReplOfFormulaInFormula.same_
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v (P.imp_ Q)) (forall_ v (P.imp_ Q))
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ forall_ v (P.imp_ Q) = forall_ v (P.imp_ Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (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_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
rfl
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ 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
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ 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_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsReplOfFormulaInFormula.imp_
|
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v P).imp_ (forall_ v Q)) (P.imp_ (forall_ v Q))
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v P) P
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v Q) (forall_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P ((forall_ v P).imp_ (forall_ v Q)) (P.imp_ (forall_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsReplOfFormulaInFormula.diff_
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v P) P
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ forall_ v P = forall_ v P
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P = P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v P) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
rfl
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ forall_ v P = forall_ v P
|
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 P
⊢ forall_ v P = forall_ v P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
rfl
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P = P
|
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 P
⊢ P = P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsReplOfFormulaInFormula.same_
|
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v Q) (forall_ v Q)
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ forall_ v Q = forall_ v Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsReplOfFormulaInFormula (forall_ v P) P (forall_ v Q) (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
rfl
|
case h1.a.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ forall_ v Q = forall_ 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 P
⊢ forall_ v Q = forall_ v Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
exact T_19_1 P v h1
|
case h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v P).iff_ P)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h2
P Q : 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_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsDeduct.axiom_
|
case h3
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
case h3.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h3
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_left
|
[1283, 1]
|
[1301, 26]
|
apply IsAxiom.pred_1_
|
case h3.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h3.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v (P.imp_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply deduction_theorem
|
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q)))
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct (∅ ∪ {P.imp_ (forall_ v Q)}) (forall_ v (P.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct (∅ ∪ {P.imp_ (forall_ v Q)}) (forall_ v (P.imp_ Q))
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (forall_ 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 P
⊢ IsDeduct (∅ ∪ {P.imp_ (forall_ v Q)}) (forall_ v (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply generalization
|
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (forall_ v (P.imp_ Q))
|
case h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (P.imp_ Q)
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ∀ H ∈ {P.imp_ (forall_ v Q)}, ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (forall_ v (P.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply deduction_theorem
|
case h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (P.imp_ Q)
|
case h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct {P.imp_ (forall_ v Q)} (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply specId v
|
case h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) Q
|
case h1.h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (forall_ v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply IsDeduct.mp_ P
|
case h1.h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (forall_ v Q)
|
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (P.imp_ (forall_ v Q))
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply IsDeduct.assume_
|
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (P.imp_ (forall_ v Q))
|
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P.imp_ (forall_ v Q) ∈ {P.imp_ (forall_ v Q)} ∪ {P}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) (P.imp_ (forall_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp
|
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P.imp_ (forall_ v Q) ∈ {P.imp_ (forall_ v Q)} ∪ {P}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P.imp_ (forall_ v Q) ∈ {P.imp_ (forall_ v Q)} ∪ {P}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
apply IsDeduct.assume_
|
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) P
|
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P ∈ {P.imp_ (forall_ v Q)} ∪ {P}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ({P.imp_ (forall_ v Q)} ∪ {P}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp
|
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P ∈ {P.imp_ (forall_ v Q)} ∪ {P}
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.h1.a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ P ∈ {P.imp_ (forall_ v Q)} ∪ {P}
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
intro H a1
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ∀ H ∈ {P.imp_ (forall_ v Q)}, ¬isFreeIn v H
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H ∈ {P.imp_ (forall_ v Q)}
⊢ ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ∀ H ∈ {P.imp_ (forall_ v Q)}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp at a1
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H ∈ {P.imp_ (forall_ v Q)}
⊢ ¬isFreeIn v H
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H = P.imp_ (forall_ v Q)
⊢ ¬isFreeIn v H
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H ∈ {P.imp_ (forall_ v Q)}
⊢ ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
subst a1
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H = P.imp_ (forall_ v Q)
⊢ ¬isFreeIn v H
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v (P.imp_ (forall_ v Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
H : Formula
a1 : H = P.imp_ (forall_ v Q)
⊢ ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp only [isFreeIn]
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v (P.imp_ (forall_ v Q))
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬(isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v (P.imp_ (forall_ v Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
simp
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬(isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v P
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬(isFreeIn v P ∨ ¬True ∧ isFreeIn v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21_right
|
[1304, 1]
|
[1325, 13]
|
exact h1
|
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ ¬isFreeIn v P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
apply IsDeduct.mp_ ((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
|
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q)))
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q))))
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
apply IsDeduct.mp_ ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q)))
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q)))))
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ 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.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
simp only [def_iff_]
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q)))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).and_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))))))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_ ((forall_ v (P.imp_ Q)).iff_ (P.imp_ (forall_ v Q)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
simp only [def_and_]
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).and_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))))))
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).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 ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).and_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
SC
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).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 ∅
(((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
(((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).not_).not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
exact T_19_TS_21_right P Q v h1
|
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ 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 ∅ ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_19_TS_21
|
[1328, 1]
|
[1342, 35]
|
exact T_19_TS_21_left P Q v h1
|
case a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
|
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.imp_ Q)).imp_ (P.imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Fol.lean
|
FOL.NV.T_21_1
|
[1345, 1]
|
[1370, 15]
|
apply generalization
|
x y : VarName
⊢ IsProof (forall_ x (forall_ y ((eq_ x y).imp_ (eq_ y x))))
|
case h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y ((eq_ x y).imp_ (eq_ y x)))
case h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y : VarName
⊢ IsProof (forall_ x (forall_ y ((eq_ x y).imp_ (eq_ y x))))
TACTIC:
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.