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_1_left | [654, 1] | [678, 9] | apply IsDeduct.mp_ P | case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q)
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | apply IsDeduct.mp_ ((P.imp_ Q).and_ (Q.imp_ P)) | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q) | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q))
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (P.imp_ Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp only [def_and_] | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (P.imp_ Q)) | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((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.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ 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_18_1_left | [654, 1] | [678, 9] | SC | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((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.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((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_18_1_left | [654, 1] | [678, 9] | apply specId v | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P)) | case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | apply IsDeduct.assume_ | case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp | case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | apply specId v | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P | case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | apply IsDeduct.assume_ | case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P) | case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp | case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v P ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v P, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp only [isFreeIn] | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v P) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_left | [654, 1] | [678, 9] | simp | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v P) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp only [def_iff_] | P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))) | P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ 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_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply deduction_theorem | P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))) | case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P)) | Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
v : VarName
⊢ IsProof ((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply deduction_theorem | case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P)) | case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}) ((forall_ v Q).imp_ (forall_ v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp | case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P) | case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct (∅ ∪ {forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ∪ {forall_ v Q}) (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply generalization | case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P) | case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply IsDeduct.mp_ Q | case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P)
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply IsDeduct.mp_ ((P.imp_ Q).and_ (Q.imp_ P)) | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P) | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P))
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (Q.imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp only [def_and_] | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P)) | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (((P.imp_ Q).and_ (Q.imp_ P)).imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | SC | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_}
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply specId v | case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P)) | case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} ((P.imp_ Q).and_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply IsDeduct.assume_ | case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp | case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v ((P.imp_ Q).and_ (Q.imp_ P)) ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply specId v | case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q | case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} Q
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | apply IsDeduct.assume_ | case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q) | case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1
P Q : Formula
v : VarName
⊢ IsDeduct {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} (forall_ v Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp | case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))} | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1.a
P Q : Formula
v : VarName
⊢ forall_ v Q ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ∀ H ∈ {forall_ v Q, forall_ v ((P.imp_ Q).and_ (Q.imp_ P))}, ¬isFreeIn v H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp only [isFreeIn] | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P))) | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬isFreeIn v (forall_ v Q) ∧ ¬isFreeIn v (forall_ v ((P.imp_ Q).and_ (Q.imp_ P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1_right | [681, 1] | [705, 9] | simp | case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
P Q : Formula
v : VarName
⊢ ¬(¬True ∧ isFreeIn v Q) ∧ ¬(¬True ∧ ((isFreeIn v P ∨ isFreeIn v Q) ∨ isFreeIn v Q ∨ isFreeIn v P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))) | P Q : Formula
v : VarName
⊢ IsProof ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))) | case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))))
case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ 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_ ((forall_ v P).iff_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | apply IsDeduct.mp_ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))) | case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))) | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q)))))
case a.a
P Q : Formula
v : VarName
⊢ IsDeduc... | 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_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((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_18_1 | [708, 1] | [721, 23] | simp only [def_iff_] | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (forall_ v Q))))) | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp... | 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 P).imp_ (forall_ v Q))).imp_
(((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).iff_ (f... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | 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 P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_
(((forall_ v P).imp... | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_... | 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 P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).and_ (Q.imp_ P))).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | SC | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_... | 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 P).imp_ (forall_ v Q))).imp_
(((forall_ v ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_ ((forall_ v Q).imp_ (forall_ v P))).imp_
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | apply T_18_1_left | case a.a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v P).imp_ (forall_ v Q))) | 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_ ((forall_ v P).imp_ (forall_ v Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_1 | [708, 1] | [721, 23] | apply T_18_1_right | case a
P Q : Formula
v : VarName
⊢ IsDeduct ∅ ((forall_ v (P.iff_ Q)).imp_ ((forall_ v Q).imp_ (forall_ v P))) | 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_ ((forall_ v Q).imp_ (forall_ v P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | induction xs | xs : List VarName
P : Formula
⊢ IsProof ((Forall_ xs P).imp_ P) | case nil
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
case cons
P : Formula
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : IsProof ((Forall_ tail✝ P).imp_ P)
⊢ IsProof ((Forall_ (head✝ :: tail✝) P).imp_ P) | Please generate a tactic in lean4 to solve the state.
STATE:
xs : List VarName
P : Formula
⊢ IsProof ((Forall_ xs P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | case nil =>
simp only [Forall_]
apply prop_id | P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | case cons xs_hd xs_tl xs_ih =>
simp only [Forall_]
apply deduction_theorem
simp
apply IsDeduct.mp_ (Forall_ xs_tl P)
apply proof_imp_deduct
exact xs_ih
apply specId xs_hd
apply IsDeduct.assume_
simp
rfl | P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | simp only [Forall_] | P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P) | P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((Forall_ [] P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply prop_id | P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof ((List.foldr forall_ P []).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | simp only [Forall_] | P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P) | P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ (xs_hd :: xs_tl) P).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply deduction_theorem | P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P) | case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((List.foldr forall_ P (xs_hd :: xs_tl)).imp_ P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | simp | case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P | case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct (∅ ∪ {List.foldr forall_ P (xs_hd :: xs_tl)}) P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply IsDeduct.mp_ (Forall_ xs_tl P) | case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P | case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply proof_imp_deduct | case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.... | case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProo... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | exact xs_ih | case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P) | case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsProof ((Forall_ xs_tl P).imp_ P)
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {fo... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply specId xs_hd | case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P) | case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (Forall_ xs_tl P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | apply IsDeduct.assume_ | case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P)) | case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)} | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ IsDeduct {forall_ xs_hd (List.foldr forall_ P xs_tl)} (forall_ xs_hd (Forall_ xs_tl P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | simp | case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)} | case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ forall_ xs_hd (Forall_ xs_tl P) ∈ {forall_ xs_hd (List.foldr forall_ P xs_tl)}
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id | [724, 1] | [743, 8] | rfl | case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P : Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsProof ((Forall_ xs_tl P).imp_ P)
⊢ Forall_ xs_tl P = List.foldr forall_ P xs_tl
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | induction xs | xs : List VarName
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ xs P)
⊢ IsDeduct Δ P | case nil
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
case cons
P : Formula
Δ : Set Formula
head✝ : VarName
tail✝ : List VarName
tail_ih✝ : IsDeduct Δ (Forall_ tail✝ P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (head✝ :: tail✝) P)
⊢ IsDeduct Δ P | Please generate a tactic in lean4 to solve the state.
STATE:
xs : List VarName
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ xs P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | case nil =>
simp only [Forall_] at h1
simp at h1
exact h1 | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | case cons xs_hd xs_tl xs_ih =>
simp only [Forall_] at h1
simp at h1
apply xs_ih
simp only [Forall_]
apply specId xs_hd
exact h1 | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | simp only [Forall_] at h1 | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (List.foldr forall_ P [])
⊢ IsDeduct Δ P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (Forall_ [] P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | simp at h1 | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (List.foldr forall_ P [])
⊢ IsDeduct Δ P | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
⊢ IsDeduct Δ P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ (List.foldr forall_ P [])
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | exact h1 | P : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
⊢ IsDeduct Δ P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | simp only [Forall_] at h1 | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl))
⊢ IsDeduct Δ P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (Forall_ (xs_hd :: xs_tl) P)
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | simp at h1 | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl))
⊢ IsDeduct Δ P | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (List.foldr forall_ P (xs_hd :: xs_tl))
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | apply xs_ih | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ P | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (Forall_ xs_tl P) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | simp only [Forall_] | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (Forall_ xs_tl P) | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (List.foldr forall_ P xs_tl) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (Forall_ xs_tl P)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | apply specId xs_hd | P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (List.foldr forall_ P xs_tl) | case h1
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (List.foldr forall_ P xs_tl)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_spec_id' | [746, 1] | [764, 13] | exact h1 | case h1
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
Δ : Set Formula
xs_hd : VarName
xs_tl : List VarName
xs_ih : IsDeduct Δ (Forall_ xs_tl P) → IsDeduct Δ P
h1 : IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
⊢ IsDeduct Δ (forall_ xs_hd (List.foldr forall_ P xs_tl))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | simp only [Formula.Forall_] | P : Formula
xs : List VarName
x : VarName
⊢ isBoundIn x (Forall_ xs P) ↔ x ∈ xs ∨ isBoundIn x P | P : Formula
xs : List VarName
x : VarName
⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs : List VarName
x : VarName
⊢ isBoundIn x (Forall_ xs P) ↔ x ∈ xs ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | induction xs | P : Formula
xs : List VarName
x : VarName
⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P | case nil
P : Formula
x : VarName
⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P
case cons
P : Formula
x head✝ : VarName
tail✝ : List VarName
tail_ih✝ : isBoundIn x (List.foldr forall_ P tail✝) ↔ x ∈ tail✝ ∨ isBoundIn x P
⊢ isBoundIn x (List.foldr forall_ P (head✝ :: tail✝)) ↔ x ∈ head✝ :: tail✝ ∨ isB... | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs : List VarName
x : VarName
⊢ isBoundIn x (List.foldr forall_ P xs) ↔ x ∈ xs ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | case nil =>
simp | P : Formula
x : VarName
⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x : VarName
⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | case cons xs_hd xs_tl xs_ih =>
simp
simp only [isBoundIn]
simp only [xs_ih]
tauto | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | simp | P : Formula
x : VarName
⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x : VarName
⊢ isBoundIn x (List.foldr forall_ P []) ↔ x ∈ [] ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | simp | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∈ xs_hd :: xs_tl ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | simp only [isBoundIn] | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ isBoundIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | simp only [xs_ih] | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ isBoundIn x (List.foldr forall_ P xs_tl) ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isBoundIn | [767, 1] | [781, 10] | tauto | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isBoundIn x (List.foldr forall_ P xs_tl) ↔ x ∈ xs_tl ∨ isBoundIn x P
⊢ x = xs_hd ∨ x ∈ xs_tl ∨ isBoundIn x P ↔ (x = xs_hd ∨ x ∈ xs_tl) ∨ isBoundIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | simp only [Formula.Forall_] | P : Formula
xs : List VarName
x : VarName
⊢ isFreeIn x (Forall_ xs P) ↔ x ∉ xs ∧ isFreeIn x P | P : Formula
xs : List VarName
x : VarName
⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs : List VarName
x : VarName
⊢ isFreeIn x (Forall_ xs P) ↔ x ∉ xs ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | induction xs | P : Formula
xs : List VarName
x : VarName
⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P | case nil
P : Formula
x : VarName
⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P
case cons
P : Formula
x head✝ : VarName
tail✝ : List VarName
tail_ih✝ : isFreeIn x (List.foldr forall_ P tail✝) ↔ x ∉ tail✝ ∧ isFreeIn x P
⊢ isFreeIn x (List.foldr forall_ P (head✝ :: tail✝)) ↔ x ∉ head✝ :: tail✝ ∧ isFreeIn... | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
xs : List VarName
x : VarName
⊢ isFreeIn x (List.foldr forall_ P xs) ↔ x ∉ xs ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | case nil =>
simp | P : Formula
x : VarName
⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x : VarName
⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | case cons xs_hd xs_tl xs_ih =>
simp
simp only [isFreeIn]
simp only [xs_ih]
tauto | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | simp | P : Formula
x : VarName
⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x : VarName
⊢ isFreeIn x (List.foldr forall_ P []) ↔ x ∉ [] ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | simp | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (List.foldr forall_ P (xs_hd :: xs_tl)) ↔ x ∉ xs_hd :: xs_tl ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | simp only [isFreeIn] | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ isFreeIn x (forall_ xs_hd (List.foldr forall_ P xs_tl)) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | simp only [xs_ih] | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ isFreeIn x (List.foldr forall_ P xs_tl) ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.Forall_isFreeIn | [784, 1] | [798, 10] | tauto | P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
x xs_hd : VarName
xs_tl : List VarName
xs_ih : isFreeIn x (List.foldr forall_ P xs_tl) ↔ x ∉ xs_tl ∧ isFreeIn x P
⊢ ¬x = xs_hd ∧ x ∉ xs_tl ∧ isFreeIn x P ↔ (¬x = xs_hd ∧ x ∉ xs_tl) ∧ isFreeIn x P
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | induction h1 | U V P_U P_V : Formula
l : List VarName
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_U.iff_ P_V)) | case same_
U V P_U P_V : Formula
l : List VarName
P_u✝ P_v✝ : Formula
a✝ : P_u✝ = P_v✝
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝))
case diff_
U V P_U P_V : Formula
l : List VarName
P_u✝ P_v✝ : Formula
a✝¹ : P_u✝ = U
a✝ : P_v✝ =... | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_U → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (P_U.iff_ P_V))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | case same_ h1_P h1_P' h1_1 =>
subst h1_1
simp only [def_iff_]
simp only [def_and_]
SC | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = h1_P'
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = h1_P'
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | case diff_ h1_P h1_P' h1_1 h1_2 =>
subst h1_1
subst h1_2
apply Forall_spec_id | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = U
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = U
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | all_goals
sorry | case and_
U V P_U P_V : Formula
l : List VarName
P_u✝ Q_u✝ P_v✝ Q_v✝ : Formula
a✝¹ : IsReplOfFormulaInFormula U V P_u✝ P_v✝
a✝ : IsReplOfFormulaInFormula U V Q_u✝ Q_v✝
a_ih✝¹ :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝))
a_ih... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case and_
U V P_U P_V : Formula
l : List VarName
P_u✝ Q_u✝ P_v✝ Q_v✝ : Formula
a✝¹ : IsReplOfFormulaInFormula U V P_u✝ P_v✝
a✝ : IsReplOfFormulaInFormula U V Q_u✝ Q_v✝
a_ih✝¹ :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) →
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | subst h1_1 | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = h1_P'
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P)) | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = h1_P'
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_iff_] | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P)) | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P))) | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_and_] | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P))) | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P).and_ (h1_P.imp_ h1_P)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | SC | U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P : Formula
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_P.imp_ h1_P).imp_ (h1_P.imp_ h1_P).not_).not_)
TACTIC:... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | subst h1_1 | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = U
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P')) | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : h1_P = U
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | subst h1_2 | V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P')) | P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P')) | Please generate a tactic in lean4 to solve the state.
STATE:
V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_2 : h1_P' = V
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ V)).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply Forall_spec_id | P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P')) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h2 : ∀ (v : VarName), (isFreeIn v h1_P ∨ isFreeIn v h1_P') ∧ isBoundIn v h1_P → v ∈ l
⊢ IsProof ((Forall_ l (h1_P.iff_ h1_P')).imp_ (h1_P.iff_ h1_P'))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [isBoundIn] at h2 | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v... | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v... | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v... | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | Please generate a tactic in lean4 to solve the state.
STATE:
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 :... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_iff_] | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_and_] | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | SC | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | exact h1_ih h2 | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBo... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.