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_2 | [802, 1] | [886, 10] | simp only [isBoundIn] at h2 | U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v (h1_P.imp_ h1_Q) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q'))) | U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q'))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q'))) | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')).imp_
((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q'))))
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.mp_ ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q')) | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')).imp_
((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q')))) | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q')).imp_
(((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')).imp_
((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q')))))
case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_iff_] | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q')).imp_
(((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')).imp_
((Forall_ l (U.iff_ V)).imp_ ((h1_P.imp_ h1_Q).iff_ (h1_P'.imp_ h1_Q'))))) | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_Q.imp_ h1_Q').and_ (h1_Q'.imp_ h1_Q))).imp_
(((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P').and_ (h1_P'.imp_ h1_P))).imp_
((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_
(((h1_P.imp_ h1_Q).imp_ (h1_P'.imp_ h1_Q')).and_ ((h1_P'.imp_ h1_Q').imp_ (h1_P.imp_ h1_Q)))))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_and_] | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_Q.imp_ h1_Q').and_ (h1_Q'.imp_ h1_Q))).imp_
(((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_ ((h1_P.imp_ h1_P').and_ (h1_P'.imp_ h1_P))).imp_
((Forall_ l ((U.imp_ V).and_ (V.imp_ U))).imp_
(((h1_P.imp_ h1_Q).imp_ (h1_P'.imp_ h1_Q')).and_ ((h1_P'.imp_ h1_Q').imp_ (h1_P.imp_ h1_Q)))))) | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_Q.imp_ h1_Q').imp_ (h1_Q'.imp_ h1_Q).not_).not_).imp_
(((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
((h1_P.imp_ h1_P').imp_ (h1_P'.imp_ h1_P).not_).not_).imp_
((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
(((h1_P.imp_ h1_Q).imp_ (h1_P'.imp_ h1_Q')).imp_ ((h1_P'.imp_ h1_Q').imp_ (h1_P.imp_ h1_Q)).not_).not_))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | SC | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
(((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_Q.imp_ h1_Q').imp_ (h1_Q'.imp_ h1_Q).not_).not_).imp_
(((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
((h1_P.imp_ h1_P').imp_ (h1_P'.imp_ h1_P).not_).not_).imp_
((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
(((h1_P.imp_ h1_Q).imp_ (h1_P'.imp_ h1_Q')).imp_ ((h1_P'.imp_ h1_Q').imp_ (h1_P.imp_ h1_Q)).not_).not_))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h1_ih_2 | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q')) | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | intro v a2 | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a2 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q
β’ v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h2 v | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a2 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q
β’ v β l | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a2 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | tauto | case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a2 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h1_ih_1 | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ IsDeduct β
((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | intro v a1 | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h2 v | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ v β l | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | cases a1 | case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) | case a.intro
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
leftβ : isFreeIn v U β¨ isFreeIn v V
rightβ : isBoundIn v h1_P
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | constructor | U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) | case left
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isFreeIn v U β¨ isFreeIn v V
case right
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P β¨ isBoundIn v h1_Q |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | exact a1_left | case left
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isFreeIn v U β¨ isFreeIn v V | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | left | case right
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P β¨ isBoundIn v h1_Q | case right.h
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | exact a1_right | case right.h
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_Q β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (isBoundIn v h1_P β¨ isBoundIn v h1_Q) β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [isBoundIn] at h2 | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v (forall_ h1_x h1_P) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (v = h1_x β¨ isBoundIn v h1_P) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp at h2 | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ (v = h1_x β¨ isBoundIn v h1_P) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply deduction_theorem | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) | case h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct (β
βͺ {Forall_ l (U.iff_ V)}) ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp | case h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct (β
βͺ {Forall_ l (U.iff_ V)}) ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P')) | case h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.mp_ (forall_ h1_x (h1_P.iff_ h1_P')) | case h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P')) | case h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)}
((forall_ h1_x (h1_P.iff_ h1_P')).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P')))
case h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (forall_ h1_x (h1_P.iff_ h1_P')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply proof_imp_deduct | case h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)}
((forall_ h1_x (h1_P.iff_ h1_P')).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) | case h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((forall_ h1_x (h1_P.iff_ h1_P')).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply T_18_1 | case h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((forall_ h1_x (h1_P.iff_ h1_P')).imp_ ((forall_ h1_x h1_P).iff_ (forall_ h1_x h1_P'))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply generalization | case h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (forall_ h1_x (h1_P.iff_ h1_P')) | case h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (h1_P.iff_ h1_P')
case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ β H β {Forall_ l (U.iff_ V)}, Β¬isFreeIn h1_x H |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.mp_ (Forall_ l (U.iff_ V)) | case h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (h1_P.iff_ h1_P') | case h1.a.h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
case h1.a.h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (Forall_ l (U.iff_ V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply proof_imp_deduct | case h1.a.h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h1_ih | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P')) | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | intro v a1 | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | cases a1 | case h1.a.h1.a.h1
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P
β’ v β l | case h1.a.h1.a.h1.intro
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
leftβ : isFreeIn v U β¨ isFreeIn v V
rightβ : isBoundIn v h1_P
β’ v β l |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | case _ a1_left a1_right =>
apply h2 v a1_left
right
apply a1_right | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ v β l | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply h2 v a1_left | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ v β l | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ v = h1_x β¨ isBoundIn v h1_P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | right | U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ v = h1_x β¨ isBoundIn v h1_P | case h
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply a1_right | case h
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
v : VarName
a1_left : isFreeIn v U β¨ isFreeIn v V
a1_right : isBoundIn v h1_P
β’ isBoundIn v h1_P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | apply IsDeduct.assume_ | case h1.a.h1.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ IsDeduct {Forall_ l (U.iff_ V)} (Forall_ l (U.iff_ V)) | case h1.a.h1.a.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Forall_ l (U.iff_ V) β {Forall_ l (U.iff_ V)} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp | case h1.a.h1.a.a
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Forall_ l (U.iff_ V) β {Forall_ l (U.iff_ V)} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | intro H a1 | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ β H β {Forall_ l (U.iff_ V)}, Β¬isFreeIn h1_x H | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
H : Formula
a1 : H β {Forall_ l (U.iff_ V)}
β’ Β¬isFreeIn h1_x H |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp at a1 | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
H : Formula
a1 : H β {Forall_ l (U.iff_ V)}
β’ Β¬isFreeIn h1_x H | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
H : Formula
a1 : H = Forall_ l (U.iff_ V)
β’ Β¬isFreeIn h1_x H |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | subst a1 | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
H : Formula
a1 : H = Forall_ l (U.iff_ V)
β’ Β¬isFreeIn h1_x H | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬isFreeIn h1_x (Forall_ l (U.iff_ V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [Forall_isFreeIn] | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬isFreeIn h1_x (Forall_ l (U.iff_ V)) | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x (U.iff_ V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_iff_] | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x (U.iff_ V)) | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x ((U.imp_ V).and_ (V.imp_ U))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [def_and_] | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x ((U.imp_ V).and_ (V.imp_ U))) | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x ((U.imp_ V).imp_ (V.imp_ U).not_).not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | simp only [isFreeIn] | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ isFreeIn h1_x ((U.imp_ V).imp_ (V.imp_ U).not_).not_) | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ ((isFreeIn h1_x U β¨ isFreeIn h1_x V) β¨ isFreeIn h1_x V β¨ isFreeIn h1_x U)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | sorry | case h1.a.h2
U V P_U P_V : Formula
l : List VarName
h1_x : VarName
h1_P h1_P' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_ih :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v h1_P β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h2 : β (v : VarName), isFreeIn v U β¨ isFreeIn v V β v = h1_x β¨ isBoundIn v h1_P β v β l
β’ Β¬(h1_x β l β§ ((isFreeIn h1_x U β¨ isFreeIn h1_x V) β¨ isFreeIn h1_x V β¨ isFreeIn h1_x U)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_2 | [802, 1] | [886, 10] | sorry | case exists_
U V P_U P_V : Formula
l : List VarName
xβ : VarName
P_uβ P_vβ : Formula
aβ : IsReplOfFormulaInFormula U V P_uβ P_vβ
a_ihβ :
(β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_uβ β v β l) β
IsProof ((Forall_ l (U.iff_ V)).imp_ (P_uβ.iff_ P_vβ))
h2 : β (v : VarName), (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v (exists_ xβ P_uβ) β v β l
β’ IsProof ((Forall_ l (U.iff_ V)).imp_ ((exists_ xβ P_uβ).iff_ (exists_ xβ P_vβ))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | apply
IsDeduct.mp_
(Forall_ ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList (U.iff_ V)) | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsProof (P_U.iff_ P_V) | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
((Forall_ ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList (U.iff_ V)).imp_ (P_U.iff_ P_V))
case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(Forall_ ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList (U.iff_ V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | apply T_18_2 U V P_U P_V ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList h1 | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
((Forall_ ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList (U.iff_ V)).imp_ (P_U.iff_ P_V)) | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ β (v : VarName),
(isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U β v β ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | intro v a1 | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ β (v : VarName),
(isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U β v β ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U
β’ v β ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U
β’ v β ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp only [isFreeIn_iff_mem_freeVarSet] at a1 | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (isFreeIn v U β¨ isFreeIn v V) β§ isBoundIn v P_U
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (v β U.freeVarSet β¨ v β V.freeVarSet) β§ isBoundIn v P_U
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp only [isBoundIn_iff_mem_boundVarSet] at a1 | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (v β U.freeVarSet β¨ v β V.freeVarSet) β§ isBoundIn v P_U
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | exact a1 | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
v : VarName
a1 : (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet
β’ (v β U.freeVarSet β¨ v β V.freeVarSet) β§ v β P_U.boundVarSet | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp only [Formula.Forall_] | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(Forall_ ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList (U.iff_ V)) | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | induction ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList | case a
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) ((U.freeVarSet βͺ V.freeVarSet) β© P_U.boundVarSet).toList) | case a.nil
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) [])
case a.cons
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
headβ : VarName
tailβ : List VarName
tail_ihβ : IsDeduct β
(List.foldr forall_ (U.iff_ V) tailβ)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) (headβ :: tailβ)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | case _ =>
simp
exact h2 | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) []) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) []) | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(U.iff_ V) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | exact h2 | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
β’ IsDeduct β
(U.iff_ V) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) (hd :: tl)) | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ IsDeduct β
(forall_ hd (List.foldr forall_ (U.iff_ V) tl)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | apply generalization | U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ IsDeduct β
(forall_ hd (List.foldr forall_ (U.iff_ V) tl)) | case h1
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
case h2
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ β H β β
, Β¬isFreeIn hd H |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | exact ih | case h1
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ IsDeduct β
(List.foldr forall_ (U.iff_ V) tl) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_3 | [889, 1] | [913, 13] | simp | case h2
U V P_U P_V : Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
hd : VarName
tl : List VarName
ih : IsDeduct β
(List.foldr forall_ (U.iff_ V) tl)
β’ β H β β
, Β¬isFreeIn hd H | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | apply IsDeduct.mp_ P_U | U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ P_V | case a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (P_U.imp_ P_V)
case a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ P_U |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | apply IsDeduct.mp_ (P_U.iff_ P_V) | case a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (P_U.imp_ P_V) | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ ((P_U.iff_ P_V).imp_ (P_U.imp_ P_V))
case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (P_U.iff_ P_V) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | simp only [def_iff_] | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ ((P_U.iff_ P_V).imp_ (P_U.imp_ P_V)) | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (((P_U.imp_ P_V).and_ (P_V.imp_ P_U)).imp_ (P_U.imp_ P_V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | simp only [def_and_] | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (((P_U.imp_ P_V).and_ (P_V.imp_ P_U)).imp_ (P_U.imp_ P_V)) | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (((P_U.imp_ P_V).imp_ (P_V.imp_ P_U).not_).not_.imp_ (P_U.imp_ P_V)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | SC | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (((P_U.imp_ P_V).imp_ (P_V.imp_ P_U).not_).not_.imp_ (P_U.imp_ P_V)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | apply proof_imp_deduct | case a.a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ (P_U.iff_ P_V) | case a.a.h1
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsProof (P_U.iff_ P_V) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | exact C_18_3 U V P_U P_V h1 h2 | case a.a.h1
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsProof (P_U.iff_ P_V) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.C_18_4 | [917, 1] | [935, 13] | exact h3 | case a
U V P_U P_V : Formula
Ξ : Set Formula
h1 : IsReplOfFormulaInFormula U V P_U P_V
h2 : IsProof (U.iff_ V)
h3 : IsDeduct Ξ P_U
β’ IsDeduct Ξ P_U | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_exists_] | P : Formula
v : VarName
β’ IsProof ((forall_ v P).iff_ (exists_ v P.not_).not_) | P : Formula
v : VarName
β’ IsProof ((forall_ v P).iff_ (forall_ v P.not_.not_).not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply C_18_4 P P.not_.not_ ((forall_ v P).iff_ (forall_ v P).not_.not_) | P : Formula
v : VarName
β’ IsProof ((forall_ v P).iff_ (forall_ v P.not_.not_).not_.not_) | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).iff_ (forall_ v P).not_.not_)
((forall_ v P).iff_ (forall_ v P.not_.not_).not_.not_)
case h2
P : Formula
v : VarName
β’ IsProof (P.iff_ P.not_.not_)
case h3
P : Formula
v : VarName
β’ IsDeduct β
((forall_ v P).iff_ (forall_ v P).not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_iff_] | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).iff_ (forall_ v P).not_.not_)
((forall_ v P).iff_ (forall_ v P.not_.not_).not_.not_) | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).and_ ((forall_ v P).not_.not_.imp_ (forall_ v P)))
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).and_ ((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_and_] | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).and_ ((forall_ v P).not_.not_.imp_ (forall_ v P)))
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).and_ ((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P))) | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_).not_
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).imp_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_).not_
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).imp_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_).not_ | case h1.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_)
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).imp_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.imp_ | case h1.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_
(((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_)
(((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_).imp_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_) | case h1.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).imp_ (forall_ v P).not_.not_)
((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_)
case h1.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.imp_ | case h1.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).imp_ (forall_ v P).not_.not_)
((forall_ v P).imp_ (forall_ v P.not_.not_).not_.not_) | case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P)
case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_.not_ (forall_ v P.not_.not_).not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.same_ | case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P) | case h1.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_.not_ (forall_ v P.not_.not_).not_.not_ | case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_ (forall_ v P.not_.not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_ (forall_ v P.not_.not_).not_ | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.forall_ | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P.not_.not_) | case h1.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.diff_ | case h1.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_ | case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P
case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)).not_ | case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).not_.not_.imp_ (forall_ v P))
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.imp_ | case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ ((forall_ v P).not_.not_.imp_ (forall_ v P))
((forall_ v P.not_.not_).not_.not_.imp_ (forall_ v P)) | case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_.not_ (forall_ v P.not_.not_).not_.not_
case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_.not_ (forall_ v P.not_.not_).not_.not_ | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_ (forall_ v P.not_.not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.not_ | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P).not_ (forall_ v P.not_.not_).not_ | case h1.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.forall_ | case h1.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P.not_.not_) | case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.diff_ | case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_ | case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P
case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | apply IsReplOfFormulaInFormula.same_ | case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P) | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | rfl | case h1.a.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_iff_] | case h2
P : Formula
v : VarName
β’ IsProof (P.iff_ P.not_.not_) | case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).and_ (P.not_.not_.imp_ P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_and_] | case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).and_ (P.not_.not_.imp_ P)) | case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).imp_ (P.not_.not_.imp_ P).not_).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | SC | case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).imp_ (P.not_.not_.imp_ P).not_).not_ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_iff_] | case h3
P : Formula
v : VarName
β’ IsDeduct β
((forall_ v P).iff_ (forall_ v P).not_.not_) | case h3
P : Formula
v : VarName
β’ IsDeduct β
(((forall_ v P).imp_ (forall_ v P).not_.not_).and_ ((forall_ v P).not_.not_.imp_ (forall_ v P))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_5 | [938, 1] | [980, 7] | simp only [def_and_] | case h3
P : Formula
v : VarName
β’ IsDeduct β
(((forall_ v P).imp_ (forall_ v P).not_.not_).and_ ((forall_ v P).not_.not_.imp_ (forall_ v P))) | case h3
P : Formula
v : VarName
β’ IsDeduct β
(((forall_ v P).imp_ (forall_ v P).not_.not_).imp_ ((forall_ v P).not_.not_.imp_ (forall_ v P)).not_).not_ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.