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_21_1 | [1345, 1] | [1370, 15] | apply generalization | case h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y ((eq_ x y).imp_ (eq_ y x))) | case h1.h1
x y : VarName
⊢ IsDeduct ∅ ((eq_ x y).imp_ (eq_ y x))
case h1.h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y ((eq_ x y).imp_ (eq_ y x)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply IsDeduct.mp_ (eq_ y y) | case h1.h1
x y : VarName
⊢ IsDeduct ∅ ((eq_ x y).imp_ (eq_ y x)) | case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))
case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ (eq_ y y) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
x y : VarName
⊢ IsDeduct ∅ ((eq_ x y).imp_ (eq_ y x))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply IsDeduct.mp_ (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))) | case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x))) | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))).imp_ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x))))
case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅ (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | simp only [def_iff_] | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))).imp_ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))) | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ (((eq_ y x).imp_ (eq_ y y)).and_ ((eq_ y y).imp_ (eq_ y x)))).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))).imp_ ((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | simp only [def_and_] | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ (((eq_ y x).imp_ (eq_ y y)).and_ ((eq_ y y).imp_ (eq_ y x)))).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))) | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).imp_ (eq_ x y).not_).not_.imp_
(((eq_ y x).imp_ (eq_ y y)).imp_ ((eq_ y y).imp_ (eq_ y x)).not_).not_).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).and_ (eq_ x y)).imp_ (((eq_ y x).imp_ (eq_ y y)).and_ ((eq_ y y).imp_ (eq_ y x)))).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | SC | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).imp_ (eq_ x y).not_).not_.imp_
(((eq_ y x).imp_ (eq_ y y)).imp_ ((eq_ y y).imp_ (eq_ y x)).not_).not_).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x)))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅
((((eq_ y y).imp_ (eq_ x y).not_).not_.imp_
(((eq_ y x).imp_ (eq_ y y)).imp_ ((eq_ y y).imp_ (eq_ y x)).not_).not_).imp_
((eq_ y y).imp_ ((eq_ x y).imp_ (eq_ y x))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply specId y | case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅ (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))) | case h1.h1.a.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a
x y : VarName
⊢ IsDeduct ∅ (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply specId y | case h1.h1.a.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))) | case h1.h1.a.a.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply specId x | case h1.h1.a.a.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))) | case h1.h1.a.a.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply specId y | case h1.h1.a.a.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))))) | case h1.h1.a.a.h1.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅
(forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply IsDeduct.axiom_ | case h1.h1.a.a.h1.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅
(forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))))) | case h1.h1.a.a.h1.h1.h1.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a.h1.h1.h1.h1
x y : VarName
⊢ IsDeduct ∅
(forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | exact IsAxiom.eq_2_eq_ y x y y | case h1.h1.a.a.h1.h1.h1.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y))))))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.a.h1.h1.h1.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (forall_ x (forall_ y (forall_ y (((eq_ y y).and_ (eq_ x y)).imp_ ((eq_ y x).iff_ (eq_ y y)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply specId y | case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ (eq_ y y) | case h1.h1.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (eq_ y y)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a
x y : VarName
⊢ IsDeduct ∅ (eq_ y y)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | apply IsDeduct.axiom_ | case h1.h1.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (eq_ y y)) | case h1.h1.a.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (eq_ y y)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.h1
x y : VarName
⊢ IsDeduct ∅ (forall_ y (eq_ y y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | exact IsAxiom.eq_1_ y | case h1.h1.a.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (eq_ y y)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.a.h1.a
x y : VarName
⊢ IsAxiom (forall_ y (eq_ y y))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | intro H a1 | case h1.h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H | case h1.h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | simp at a1 | case h1.h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | intro H a1 | case h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H | case h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
x y : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_1 | [1345, 1] | [1370, 15] | simp at a1 | case h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
x y : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply generalization | x y z : VarName
⊢ IsProof (forall_ x (forall_ y (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))) | case h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))
case h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : VarName
⊢ IsProof (forall_ x (forall_ y (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply generalization | case h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))) | case h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))
case h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply generalization | case h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))) | case h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))
case h1.h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn z H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply IsDeduct.mp_ (eq_ z z) | case h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)) | case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ ((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))
case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ (eq_ z z) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply IsDeduct.mp_ (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))) | case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ ((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))) | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))
case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ ((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | simp only [def_iff_] | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))) | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ (((eq_ x z).imp_ (eq_ y z)).and_ ((eq_ y z).imp_ (eq_ x z)))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | simp only [def_and_] | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ (((eq_ x z).imp_ (eq_ y z)).and_ ((eq_ y z).imp_ (eq_ x z)))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z)))) | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).imp_ (eq_ z z).not_).not_.imp_
(((eq_ x z).imp_ (eq_ y z)).imp_ ((eq_ y z).imp_ (eq_ x z)).not_).not_).imp_
((eq_ z z).imp_ (((eq_ x y).imp_ (eq_ y z).not_).not_.imp_ (eq_ x z)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).and_ (eq_ z z)).imp_ (((eq_ x z).imp_ (eq_ y z)).and_ ((eq_ y z).imp_ (eq_ x z)))).imp_
((eq_ z z).imp_ (((eq_ x y).and_ (eq_ y z)).imp_ (eq_ x z))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | SC | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).imp_ (eq_ z z).not_).not_.imp_
(((eq_ x z).imp_ (eq_ y z)).imp_ ((eq_ y z).imp_ (eq_ x z)).not_).not_).imp_
((eq_ z z).imp_ (((eq_ x y).imp_ (eq_ y z).not_).not_.imp_ (eq_ x z)))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅
((((eq_ x y).imp_ (eq_ z z).not_).not_.imp_
(((eq_ x z).imp_ (eq_ y z)).imp_ ((eq_ y z).imp_ (eq_ x z)).not_).not_).imp_
((eq_ z z).imp_ (((eq_ x y).imp_ (eq_ y z).not_).not_.imp_ (eq_ x z))))... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply specId z | case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))) | case h1.h1.h1.a.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a
x y z : VarName
⊢ IsDeduct ∅ (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply specId y | case h1.h1.h1.a.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))) | case h1.h1.h1.a.a.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply specId z | case h1.h1.h1.a.a.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))) | case h1.h1.h1.a.a.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply specId x | case h1.h1.h1.a.a.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))))) | case h1.h1.h1.a.a.h1.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅
(forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply IsDeduct.axiom_ | case h1.h1.h1.a.a.h1.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅
(forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))))) | case h1.h1.h1.a.a.h1.h1.h1.h1.a
x y z : VarName
⊢ IsAxiom (forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.h1.h1.h1
x y z : VarName
⊢ IsDeduct ∅
(forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | exact IsAxiom.eq_2_eq_ x z y z | case h1.h1.h1.a.a.h1.h1.h1.h1.a
x y z : VarName
⊢ IsAxiom (forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z))))))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.a.h1.h1.h1.h1.a
x y z : VarName
⊢ IsAxiom (forall_ x (forall_ z (forall_ y (forall_ z (((eq_ x y).and_ (eq_ z z)).imp_ ((eq_ x z).iff_ (eq_ y z)))))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply specId z | case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ (eq_ z z) | case h1.h1.h1.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (eq_ z z)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a
x y z : VarName
⊢ IsDeduct ∅ (eq_ z z)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | apply IsDeduct.axiom_ | case h1.h1.h1.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (eq_ z z)) | case h1.h1.h1.a.h1.a
x y z : VarName
⊢ IsAxiom (forall_ z (eq_ z z)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1
x y z : VarName
⊢ IsDeduct ∅ (forall_ z (eq_ z z))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | exact IsAxiom.eq_1_ z | case h1.h1.h1.a.h1.a
x y z : VarName
⊢ IsAxiom (forall_ z (eq_ z z)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h1.a.h1.a
x y z : VarName
⊢ IsAxiom (forall_ z (eq_ z z))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | intro H a1 | case h1.h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn z H | case h1.h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn z H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn z H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | simp at a1 | case h1.h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn z H | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn z H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | intro H a1 | case h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H | case h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn y H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | simp at a1 | case h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn y H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | intro H a1 | case h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H | case h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
x y z : VarName
⊢ ∀ H ∈ ∅, ¬isFreeIn x H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_2 | [1373, 1] | [1401, 15] | simp at a1 | case h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
x y z : VarName
H : Formula
a1 : H ∈ ∅
⊢ ¬isFreeIn x H
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | induction h1 | P_r P_s : Formula
r s : VarName
h1 : IsReplOfVarInFormula r s P_r P_s
h2 : ¬isBoundIn r P_r
h3 : ¬isBoundIn s P_r
⊢ IsProof ((eq_ r s).imp_ (P_r.iff_ P_s)) | case pred_const_
P_r P_s : Formula
r s : VarName
name✝ : PredName
n✝ : ℕ
args_u✝ args_v✝ : Fin n✝ → VarName
a✝ : ∀ (i : Fin n✝), args_u✝ i = args_v✝ i ∨ args_u✝ i = r ∧ args_v✝ i = s
h2 : ¬isBoundIn r (pred_const_ name✝ (List.ofFn args_u✝))
h3 : ¬isBoundIn s (pred_const_ name✝ (List.ofFn args_u✝))
⊢ IsProof ((eq_ r s).... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
h1 : IsReplOfVarInFormula r s P_r P_s
h2 : ¬isBoundIn r P_r
h3 : ¬isBoundIn s P_r
⊢ IsProof ((eq_ r s).imp_ (P_r.iff_ P_s))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case true_ =>
simp only [def_iff_]
simp only [def_and_]
SC | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ (true_.iff_ true_)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ (true_.iff_ true_))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | all_goals
sorry | case pred_var_
P_r P_s : Formula
r s : VarName
name✝ : PredName
n✝ : ℕ
args_u✝ args_v✝ : Fin n✝ → VarName
a✝ : ∀ (i : Fin n✝), args_u✝ i = args_v✝ i ∨ args_u✝ i = r ∧ args_v✝ i = s
h2 : ¬isBoundIn r (pred_var_ name✝ (List.ofFn args_u✝))
h3 : ¬isBoundIn s (pred_var_ name✝ (List.ofFn args_u✝))
⊢ IsProof ((eq_ r s).imp_ (... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case pred_var_
P_r P_s : Formula
r s : VarName
name✝ : PredName
n✝ : ℕ
args_u✝ args_v✝ : Fin n✝ → VarName
a✝ : ∀ (i : Fin n✝), args_u✝ i = args_v✝ i ∨ args_u✝ i = r ∧ args_v✝ i = s
h2 : ¬isBoundIn r (pred_var_ name✝ (List.ofFn args_u✝))
h3 : ¬isBoundIn s (pre... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_iff_] | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ (true_.iff_ true_)) | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).and_ (true_.imp_ true_))) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ (true_.iff_ true_))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_and_] | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).and_ (true_.imp_ true_))) | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).imp_ (true_.imp_ true_).not_).not_) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).and_ (true_.imp_ true_)))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).imp_ (true_.imp_ true_).not_).not_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
h2 : ¬isBoundIn r true_
h3 : ¬isBoundIn s true_
⊢ IsProof ((eq_ r s).imp_ ((true_.imp_ true_).imp_ (true_.imp_ true_).not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply
IsDeduct.mp_
((eq_ r s).imp_ ((pred_const_ name (List.ofFn args_u)).iff_ (pred_const_ name (List.ofFn args_v)))) | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsProof ((eq_ r s).imp_ ((pred_const_ name (List... | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((pred_co... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofF... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((pred_co... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (L... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply
IsDeduct.mp_ ((eq_ r s).imp_ (And_ (List.ofFn fun (i : Fin n) => eq_ (args_u i) (args_v i)))) | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅ ((eq_ r s).imp_ ((pred_const_ ... | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((eq_ r s).imp_ (And_ (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (L... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply
IsDeduct.mp_
((And_ (List.ofFn fun (i : Fin n) => eq_ (args_u i) (args_v i))).imp_
((pred_const_ name (List.ofFn args_u)).iff_ (pred_const_ name (List.ofFn args_v)))) | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((eq_ r s).imp_ (And_ (... | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_iff_] | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_and_] | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(((And_ (List.ofFn fun... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply Forall_spec_id' (List.ofFn args_v) | case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
((And_ (List.ofFn fun ... | case a.a.a.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(Forall_ (List.ofFn... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ nam... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply Forall_spec_id' (List.ofFn args_u) | case a.a.a.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(Forall_ (List.ofFn... | case a.a.a.h1.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(Forall_ (List.o... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsDeduct.axiom_ | case a.a.a.h1.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅
(Forall_ (List.o... | case a.a.a.h1.h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsAxiom
(Forall_ (List.of... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a.h1.h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_cons... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | exact IsAxiom.eq_2_pred_const_ name n args_u args_v | case a.a.a.h1.h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsAxiom
(Forall_ (List.of... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a.a.h1.h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_co... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | clear h2 | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.... | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h2 : ¬isBoundIn r (pred_const_ name (List.ofFn args_u))
h3 : ¬isBoundIn s (pred_const_ name ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | clear h3 | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
h3 : ¬isBoundIn s (pred_const_ name (List.ofFn args_u))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [And_] | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (And_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | induction n | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | case a.a.zero
P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
case a.a.succ
P_r P_s : Formula
r s : VarName
name :... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
args_u args_v : Fin n → VarName
h1_1 : ∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ =>
simp
SC | P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
TACTIC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp | P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i)))) | P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ true_) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
TACTIC... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ true_) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
args_u args_v : Fin 0 → VarName
h1_1 : ∀ (i : Fin 0), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s
⊢ IsDeduct ∅ ((eq_ r s).imp_ true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
h1_1 :... | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
h1_1 :... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply
IsDeduct.mp_
((eq_ r s).imp_
(List.foldr and_ true_
(List.ofFn fun (i : Fin n) => eq_ (args_u i.succ) (args_v i.succ)))) | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
h1_1 :... | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsDeduct.mp_ ((eq_ r s).imp_ (eq_ (args_u 0) (args_v 0))) | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName... | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_and_] | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | specialize h1_1 0 | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | cases h1_1 | case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNa... | case a.a.inl
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → V... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ c1 =>
apply IsDeduct.mp_ (eq_ (args_u 0) (args_v 0))
case _ =>
SC
case _ =>
simp only [c1]
apply specId (args_v 0)
apply IsDeduct.axiom_
apply IsAxiom.eq_1_ | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ c1 =>
cases c1
case _ c1_left c1_right =>
subst c1_left
subst c1_right
SC | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsDeduct.mp_ (eq_ (args_u 0) (args_v 0)) | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ =>
SC | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ =>
simp only [c1]
apply specId (args_v 0)
apply IsDeduct.axiom_
apply IsAxiom.eq_1_ | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [c1] | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply specId (args_v 0) | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | case h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNam... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsDeduct.axiom_ | case h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarNam... | case h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarN... | Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsAxiom.eq_1_ | case h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarN... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | cases c1 | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1 : a... | case intro
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → Var... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | case _ c1_left c1_right =>
subst c1_left
subst c1_right
SC | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1_lef... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | subst c1_left | P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName
c1_lef... | P_r P_s : Formula
s : VarName
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
c1_right : args_v 0 = s
ih :
∀ (args_u_1 args_v : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v i ∨ args_u_1 i = args_u 0 ∧ args_v i = s) →
IsDeduct ∅ ((eq_ (args_u 0) s).imp_ (List.foldr and_ true_ (List.ofFn ... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | subst c1_right | P_r P_s : Formula
s : VarName
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
c1_right : args_v 0 = s
ih :
∀ (args_u_1 args_v : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v i ∨ args_u_1 i = args_u 0 ∧ args_v i = s) →
IsDeduct ∅ ((eq_ (args_u 0) s).imp_ (List.foldr and_ true_ (List.ofFn ... | P_r P_s : Formula
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
ih :
∀ (args_u_1 args_v_1 : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v_1 i ∨ args_u_1 i = args_u 0 ∧ args_v_1 i = args_v 0) →
IsDeduct ∅
((eq_ (args_u 0) (args_v 0)).imp_ (List.foldr and_ true_ (List.ofFn fun i ... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
s : VarName
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
c1_right : args_v 0 = s
ih :
∀ (args_u_1 args_v : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v i ∨ args_u_1 i = args_u 0 ∧ args_v i = s) →
IsDeduct ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | P_r P_s : Formula
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
ih :
∀ (args_u_1 args_v_1 : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v_1 i ∨ args_u_1 i = args_u 0 ∧ args_v_1 i = args_v 0) →
IsDeduct ∅
((eq_ (args_u 0) (args_v 0)).imp_ (List.foldr and_ true_ (List.ofFn fun i ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
name : PredName
n : ℕ
args_u args_v : Fin (n + 1) → VarName
ih :
∀ (args_u_1 args_v_1 : Fin n → VarName),
(∀ (i : Fin n), args_u_1 i = args_v_1 i ∨ args_u_1 i = args_u 0 ∧ args_v_1 i = args_v 0) →
IsDeduct ∅
((eq_ (args_u... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply ih | case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → VarName... | case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → Va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | intro i | case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → Va... | case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → Va... | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply h1_1 | case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => eq_ (args_u i) (args_v i))))
args_u args_v : Fin (n + 1) → Va... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1_1
P_r P_s : Formula
r s : VarName
name : PredName
n : ℕ
ih :
∀ (args_u args_v : Fin n → VarName),
(∀ (i : Fin n), args_u i = args_v i ∨ args_u i = r ∧ args_v i = s) →
IsDeduct ∅ ((eq_ r s).imp_ (List.foldr and_ true_ (List.ofFn fun i => ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [isBoundIn] at h2 | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u.not_
h3 : ¬isBoundIn s P_u.not_
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u.not_
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u.not_
h3 : ¬isBoundIn s P_u.not_
⊢ IsProof ((eq_ r s).imp_ (P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [isBoundIn] at h3 | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u.not_
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u.not_
⊢ IsProof ((eq_ r s).imp_ (P_u.not... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | specialize h1_ih h2 h3 | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_ih : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | apply IsDeduct.mp_ ((eq_ r s).imp_ (P_u.iff_ P_v)) | P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)) | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅ (((eq_ r s).imp_ (P_u.iff_ P_v)).imp_ ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_)))
case a
P_r P_s : Formula
r s : VarNa... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsProof ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_iff_] | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅ (((eq_ r s).imp_ (P_u.iff_ P_v)).imp_ ((eq_ r s).imp_ (P_u.not_.iff_ P_v.not_))) | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).and_ (P_v.imp_ P_u))).imp_
((eq_ r s).imp_ ((P_u.not_.imp_ P_v.not_).and_ (... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅ (((eq_ r s).imp_ (P_u.iff_ P_v)).imp_ ((eq_ r s).imp_ (P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [def_and_] | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).and_ (P_v.imp_ P_u))).imp_
((eq_ r s).imp_ ((P_u.not_.imp_ P_v.not_).and_ (... | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).imp_ (P_v.imp_ P_u).not_).not_).imp_
((eq_ r s).imp_ ((P_u.not_.imp_ P_v.no... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).and_ (P_v.imp_ P_u))... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | SC | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).imp_ (P_v.imp_ P_u).not_).not_).imp_
((eq_ r s).imp_ ((P_u.not_.imp_ P_v.no... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅
(((eq_ r s).imp_ ((P_u.imp_ P_v).imp_ (P_v.imp_ P_u).... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | exact h1_ih | case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (P_u.iff_ P_v)) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
P_r P_s : Formula
r s : VarName
P_u P_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h2 : ¬isBoundIn r P_u
h3 : ¬isBoundIn s P_u
h1_ih : IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
⊢ IsDeduct ∅ ((eq_ r s).imp_ (P_u.iff_ P_v))
TACTIC:
|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_21_8 | [1404, 1] | [1543, 10] | simp only [isBoundIn] at h2 | P_r P_s : Formula
r s : VarName
P_u Q_u P_v Q_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_2 : IsReplOfVarInFormula r s Q_u Q_v
h1_ih_1 : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h1_ih_2 : ¬isBoundIn r Q_u → ¬isBoundIn s Q_u → IsProof ((eq_ r s).imp_ (Q_u.iff_ Q_v))
h2 : ¬... | P_r P_s : Formula
r s : VarName
P_u Q_u P_v Q_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_2 : IsReplOfVarInFormula r s Q_u Q_v
h1_ih_1 : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h1_ih_2 : ¬isBoundIn r Q_u → ¬isBoundIn s Q_u → IsProof ((eq_ r s).imp_ (Q_u.iff_ Q_v))
h2 : ¬... | Please generate a tactic in lean4 to solve the state.
STATE:
P_r P_s : Formula
r s : VarName
P_u Q_u P_v Q_v : Formula
h1_1 : IsReplOfVarInFormula r s P_u P_v
h1_2 : IsReplOfVarInFormula r s Q_u Q_v
h1_ih_1 : ¬isBoundIn r P_u → ¬isBoundIn s P_u → IsProof ((eq_ r s).imp_ (P_u.iff_ P_v))
h1_ih_2 : ¬isBoundIn r Q_u → ¬isB... |
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