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 |
|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | SC | case h3
P : Formula
v : VarName
⊢ IsDeduct ∅ (((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_).not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp only [Similar] at h1 | P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | cases h1 | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | case intro
P_u P_v : Formula
u v : VarName
left✝ : ¬isFreeIn v P_u
right✝ :
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | cases h1_right | P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right :
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | case intro
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
left✝ : ¬isFreeIn u P_v
right✝ : fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | cases h1_right_right | P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right : fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | case intro
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
left✝ : fastAdmits u v P_u
right✝ : fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | cases h1_right_right_right | P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right : fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | case intro
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
left✝ : fastAdmits v u P_v
right✝ : P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | cases h1_right_right_right_right | P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right : P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | case intro
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
left✝ : P_v = fastReplaceFree u v P_u
right✝ : P_u = fastReplaceFree v u P_v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply IsDeduct.mp_ ((forall_ v P_v).imp_ (forall_ u P_u)) | P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ IsProof ((f... | case a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ IsDe... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply IsDeduct.mp_ ((forall_ u P_u).imp_ (forall_ v P_v)) | case a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ IsDe... | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp only [def_iff_] | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp only [def_and_] | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | SC | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply deduction_theorem | case a.a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ Is... | case a.a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢... | case a.a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply generalization | case a.a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢... | case a.a.h1.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | subst h1_right_right_right_right_left | case a.a.h1.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h1
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v P_u)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply spec | case a.a.h1.h1
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v P_u)
... | case a.a.h1.h1.h1
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply IsDeduct.assume_ | case a.a.h1.h1.h1
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v P_... | case a.a.h1.h1.h1.a
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.a.h1.h1.h1.a
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v ... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | exact h1_right_right_left | case a.a.h1.h1.h2
P_u : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_right_left : fastAdmits u v P_u
h1_right_left : ¬isFreeIn u (fastReplaceFree u v P_u)
h1_right_right_right_left : fastAdmits v u (fastReplaceFree u v P_u)
h1_right_right_right_right_right : P_u = fastReplaceFree v u (fastReplaceFree u v P_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | intro H a1 | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp at a1 | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | subst a1 | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp only [isFreeIn] | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | intro _ | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | exact h1_left | case a.a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply deduction_theorem | case a
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ IsDe... | case a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ I... | case a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply generalization | case a.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
⊢ I... | case a.h1.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | subst h1_right_right_right_right_right | case a.h1.h1
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h1
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v)
⊢ I... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply spec | case a.h1.h1
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v)
⊢ I... | case a.h1.h1.h1
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v)
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | apply IsDeduct.assume_ | case a.h1.h1.h1
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v)
... | case a.h1.h1.h1.a
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.h1.h1.h1.a
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | exact h1_right_right_right_left | case a.h1.h1.h2
P_v : Formula
u v : VarName
h1_right_left : ¬isFreeIn u P_v
h1_right_right_right_left : fastAdmits v u P_v
h1_left : ¬isFreeIn v (fastReplaceFree v u P_v)
h1_right_right_left : fastAdmits u v (fastReplaceFree v u P_v)
h1_right_right_right_right_left : P_v = fastReplaceFree u v (fastReplaceFree v u P_v)
... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | intro H a1 | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp at a1 | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | subst a1 | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp only [isFreeIn] | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | simp | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | intro _ | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_6 | [983, 1] | [1036, 36] | exact h1_right_left | case a.h1.h2
P_u P_v : Formula
u v : VarName
h1_left : ¬isFreeIn v P_u
h1_right_left : ¬isFreeIn u P_v
h1_right_right_left : fastAdmits u v P_u
h1_right_right_right_left : fastAdmits v u P_v
h1_right_right_right_right_left : P_v = fastReplaceFree u v P_u
h1_right_right_right_right_right : P_u = fastReplaceFree v u P_v
... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_7 | [1040, 1] | [1051, 13] | apply C_18_4 (forall_ u P_u) (forall_ v P_v) Q Q' Δ h2 | P_u P_v Q Q' : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (forall_ u P_u) (forall_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q' | case h2
P_u P_v Q Q' : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (forall_ u P_u) (forall_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v))
case h3
P_u P_v Q Q' : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormula... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_7 | [1040, 1] | [1051, 13] | apply T_18_6 P_u P_v u v h3 | case h2
P_u P_v Q Q' : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (forall_ u P_u) (forall_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((forall_ u P_u).iff_ (forall_ v P_v)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_7 | [1040, 1] | [1051, 13] | exact h1 | case h3
P_u P_v Q Q' : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (forall_ u P_u) (forall_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | simp only [Similar] at * | P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u.not_ ∧
¬isFreeIn u P_v.not_ ∧
fastAdmits u v P_u.not_ ∧
fastAdmits v u P_v.not_ ∧ P_v.not_ = fa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | simp only [isFreeIn] at * | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u.not_ ∧
¬isFreeIn u P_v.not_ ∧
fastAdmits u v P_u.not_ ∧
fastAdmits v u P_v.not_ ∧ P_v.not_ = fa... | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u.not_ ∧
fastAdmits v u P_v.not_ ∧ P_v.not_ = fastReplaceF... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | simp only [fastAdmits] at * | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u ∧ fastAdmits v u P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmits u v P_u.not_ ∧
fastAdmits v u P_v.not_ ∧ P_v.not_ = fastReplaceF... | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u.not_ ∧
fastAdmitsAux v u ∅ P_v.not_ ∧ P_v... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | simp only [fastAdmitsAux] at * | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u.not_ ∧
fastAdmitsAux v u ∅ P_v.not_ ∧ P_v... | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧
fastAdmitsAux v u ∅ P_v ∧ P_v.not_ = fa... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | simp only [fastReplaceFree] at * | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧
fastAdmitsAux v u ∅ P_v ∧ P_v.not_ = fa... | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧
fastAdmitsAux v u ∅ P_v ∧ P_v.not_ = (f... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.similar_not | [1054, 1] | [1065, 8] | tauto | P_u P_v : Formula
u v : VarName
h1 :
¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧ fastAdmitsAux v u ∅ P_v ∧ P_v = fastReplaceFree u v P_u ∧ P_u = fastReplaceFree v u P_v
⊢ ¬isFreeIn v P_u ∧
¬isFreeIn u P_v ∧
fastAdmitsAux u v ∅ P_u ∧
fastAdmitsAux v u ∅ P_v ∧ P_v.not_ = (f... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | simp only [def_exists_] | P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v)) | P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsProof ((forall_ u P_u.not_).not_.iff_ (forall_ v P_v.not_).not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | apply IsDeduct.mp_ ((forall_ u P_u.not_).iff_ (forall_ v P_v.not_)) | P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsProof ((forall_ u P_u.not_).not_.iff_ (forall_ v P_v.not_).not_) | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
(((forall_ u P_u.not_).iff_ (forall_ v P_v.not_)).imp_ ((forall_ u P_u.not_).not_.iff_ (forall_ v P_v.not_).not_))
case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅ ((forall_ u P_u.not_).iff_ (forall_ v P_v.not_... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | simp only [def_iff_] | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
(((forall_ u P_u.not_).iff_ (forall_ v P_v.not_)).imp_ ((forall_ u P_u.not_).not_.iff_ (forall_ v P_v.not_).not_)) | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
((((forall_ u P_u.not_).imp_ (forall_ v P_v.not_)).and_ ((forall_ v P_v.not_).imp_ (forall_ u P_u.not_))).imp_
(((forall_ u P_u.not_).not_.imp_ (forall_ v P_v.not_).not_).and_
((forall_ v P_v.not_).not_.imp_ (forall_ u P_u.no... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | simp only [def_and_] | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
((((forall_ u P_u.not_).imp_ (forall_ v P_v.not_)).and_ ((forall_ v P_v.not_).imp_ (forall_ u P_u.not_))).imp_
(((forall_ u P_u.not_).not_.imp_ (forall_ v P_v.not_).not_).and_
((forall_ v P_v.not_).not_.imp_ (forall_ u P_u.no... | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
((((forall_ u P_u.not_).imp_ (forall_ v P_v.not_)).imp_
((forall_ v P_v.not_).imp_ (forall_ u P_u.not_)).not_).not_.imp_
(((forall_ u P_u.not_).not_.imp_ (forall_ v P_v.not_).not_).imp_
((forall_ v P_v.not_).not... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | SC | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅
((((forall_ u P_u.not_).imp_ (forall_ v P_v.not_)).imp_
((forall_ v P_v.not_).imp_ (forall_ u P_u.not_)).not_).not_.imp_
(((forall_ u P_u.not_).not_.imp_ (forall_ v P_v.not_).not_).imp_
((forall_ v P_v.not_).not... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | apply T_18_6 | case a
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ IsDeduct ∅ ((forall_ u P_u.not_).iff_ (forall_ v P_v.not_)) | case a.h1
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_8 | [1068, 1] | [1083, 37] | exact similar_not P_u P_v u v h1 | case a.h1
P_u P_v : Formula
u v : VarName
h1 : Similar P_u P_v u v
⊢ Similar P_u.not_ P_v.not_ u v | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T18_9 | [1086, 1] | [1098, 13] | apply C_18_4 (exists_ u P_u) (exists_ v P_v) Q Q' Δ h2 | Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q' | case h2
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v))
case h3
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormula... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T18_9 | [1086, 1] | [1098, 13] | exact T_18_8 P_u P_v u v h3 | case h2
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsProof ((exists_ u P_u).iff_ (exists_ v P_v)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T18_9 | [1086, 1] | [1098, 13] | exact h1 | case h3
Q Q' P_u P_v : Formula
u v : VarName
Δ : Set Formula
h1 : IsDeduct Δ Q
h2 : IsReplOfFormulaInFormula (exists_ u P_u) (exists_ v P_v) Q Q'
h3 : Similar P_u P_v u v
⊢ IsDeduct Δ Q | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply IsDeduct.mp_ ((forall_ v P).imp_ P) | P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsProof ((forall_ v P).iff_ P) | case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P))
case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply IsDeduct.mp_ (P.imp_ (forall_ v P)) | case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)) | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P)))
case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (P.imp_ (forall_ v P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | simp only [def_iff_] | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ ((forall_ v P).iff_ P))) | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P))))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | simp only [def_and_] | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_ (((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).and_ (P.imp_ (forall_ v P))))) | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_
(((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | SC | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
((P.imp_ (forall_ v P)).imp_
(((forall_ v P).imp_ P).imp_ (((forall_ v P).imp_ P).imp_ (P.imp_ (forall_ v P)).not_).not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply IsDeduct.axiom_ | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ (P.imp_ (forall_ v P)) | case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom (P.imp_ (forall_ v P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | exact IsAxiom.pred_3_ v P h1 | case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom (P.imp_ (forall_ v P)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply IsDeduct.axiom_ | case a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅ ((forall_ v P).imp_ P) | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v P).imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply IsAxiom.pred_2_ v v P P | case a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsAxiom ((forall_ v P).imp_ P) | case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastAdmits v v P
case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastReplaceFree v v P = P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply fastAdmits_self | case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastAdmits v v P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_1 | [1101, 1] | [1119, 33] | apply fastReplaceFree_self | case a.a.a
P : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ fastReplaceFree v v P = P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | apply IsDeduct.mp_ ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))) | P : Formula
u v : VarName
⊢ IsProof ((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))) | case a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))))
case a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | apply IsDeduct.mp_ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))) | case a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))) | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P)))))
case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ v (f... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | simp only [def_iff_] | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ u (forall_ v P)).iff_ (forall_ v (forall_ u P))))) | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).and_
((forall_ v (forall_ u P)).imp_ (forall_ u (foral... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | simp only [def_and_] | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).and_
((forall_ v (forall_ u P)).imp_ (forall_ u (foral... | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ v (forall_ u P)).imp_ (forall_ u (for... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | SC | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅
(((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
(((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))).imp_
((forall_ v (forall_ u P)).imp_ (forall_ u (for... | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | apply T_17_10 | case a.a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ v (forall_ u P)).imp_ (forall_ u (forall_ v P))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_2 | [1122, 1] | [1135, 18] | apply T_17_10 | case a
P : Formula
u v : VarName
⊢ IsDeduct ∅ ((forall_ u (forall_ v P)).imp_ (forall_ v (forall_ u P))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_3 | [1138, 1] | [1149, 5] | simp only [def_exists_] | P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (exists_ v P).not_) | P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (forall_ v P.not_).not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_3 | [1138, 1] | [1149, 5] | simp only [def_iff_] | P : Formula
v : VarName
⊢ IsProof ((forall_ v P.not_).iff_ (forall_ v P.not_).not_.not_) | P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).and_ ((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_3 | [1138, 1] | [1149, 5] | simp only [def_and_] | P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).and_ ((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_))) | P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).imp_
((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)).not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_3 | [1138, 1] | [1149, 5] | SC | P : Formula
v : VarName
⊢ IsProof
(((forall_ v P.not_).imp_ (forall_ v P.not_).not_.not_).imp_
((forall_ v P.not_).not_.not_.imp_ (forall_ v P.not_)).not_).not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply deduction_theorem | P : Formula
u v : VarName
⊢ IsProof ((exists_ u (forall_ v P)).imp_ (forall_ v (exists_ u P))) | case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {exists_ u (forall_ v P)}) (forall_ v (exists_ u P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp | case h1
P : Formula
u v : VarName
⊢ IsDeduct (∅ ∪ {exists_ u (forall_ v P)}) (forall_ v (exists_ u P)) | case h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (forall_ v (exists_ u P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply generalization | case h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (forall_ v (exists_ u P)) | case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u P)
case h1.h2
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn v H |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply rule_C (forall_ v P) (exists_ u P) u {exists_ u (forall_ v P)} | case h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u P) | case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u (forall_ v P))
case h1.h1.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (exists_ u P)
case h1.h1.h3
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn u H
case h1.h1.h4
P ... |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply IsDeduct.assume_ | case h1.h1.h1
P : Formula
u v : VarName
⊢ IsDeduct {exists_ u (forall_ v P)} (exists_ u (forall_ v P)) | case h1.h1.h1.a
P : Formula
u v : VarName
⊢ exists_ u (forall_ v P) ∈ {exists_ u (forall_ v P)} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp | case h1.h1.h1.a
P : Formula
u v : VarName
⊢ exists_ u (forall_ v P) ∈ {exists_ u (forall_ v P)} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply exists_intro P u u | case h1.h1.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (exists_ u P) | case h1.h1.h2.h1
P : Formula
u v : VarName
⊢ fastAdmits u u P
case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (fastReplaceFree u u P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply fastAdmits_self | case h1.h1.h2.h1
P : Formula
u v : VarName
⊢ fastAdmits u u P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp only [fastReplaceFree_self] | case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (fastReplaceFree u u P) | case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply specId v | case h1.h1.h2.h2
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) P | case h1.h1.h2.h2.h1
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (forall_ v P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | apply IsDeduct.assume_ | case h1.h1.h2.h2.h1
P : Formula
u v : VarName
⊢ IsDeduct ({exists_ u (forall_ v P)} ∪ {forall_ v P}) (forall_ v P) | case h1.h1.h2.h2.h1.a
P : Formula
u v : VarName
⊢ forall_ v P ∈ {exists_ u (forall_ v P)} ∪ {forall_ v P} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp | case h1.h1.h2.h2.h1.a
P : Formula
u v : VarName
⊢ forall_ v P ∈ {exists_ u (forall_ v P)} ∪ {forall_ v P} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp | case h1.h1.h3
P : Formula
u v : VarName
⊢ ∀ H ∈ {exists_ u (forall_ v P)}, ¬isFreeIn u H | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u (forall_ v P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp only [def_exists_] | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u (forall_ v P)) | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P).not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp only [isFreeIn] | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u (forall_ v P).not_).not_ | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬(¬True ∧ ¬u = v ∧ isFreeIn u P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp | case h1.h1.h3
P : Formula
u v : VarName
⊢ ¬(¬True ∧ ¬u = v ∧ isFreeIn u P) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_19_4 | [1152, 1] | [1183, 9] | simp only [def_exists_] | case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (exists_ u P) | case h1.h1.h4
P : Formula
u v : VarName
⊢ ¬isFreeIn u (forall_ u P.not_).not_ |
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