url stringclasses 147
values | commit stringclasses 147
values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Fol.lean | FOL.NV.T_18_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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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... | 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')... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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')... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_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)... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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')... | 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')... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_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)... |
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')... | 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')... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_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)... |
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')... | 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')... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_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)... |
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')... | 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_ ... | Please generate a tactic in lean4 to solve the state.
STATE:
case a
U V P_U P_V : Formula
l : List VarName
h1_P h1_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)... |
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... | 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_... | Please generate a tactic in lean4 to solve the state.
STATE:
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
... |
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_... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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... | 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_ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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_ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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 ... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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 ... | 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¨ isFre... | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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¨ isFre... | 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¨ isFre... | Please generate a tactic in lean4 to solve the state.
STATE:
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_ ... |
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¨ isFre... | 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¨ isF... | Please generate a tactic in lean4 to solve the state.
STATE:
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_ ... |
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¨ isF... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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¨ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ isF... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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... |
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¨ ... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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 ... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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)... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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... | 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... | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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... | 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), isFr... | Please generate a tactic in lean4 to solve the state.
STATE:
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_... |
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 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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 ... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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 ... | 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¨ isFree... | Please generate a tactic in lean4 to solve the state.
STATE:
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.if... |
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¨ isFree... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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_ (... |
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 ... | 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 ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)... |
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 ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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_ ... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | 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¨ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ ... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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)).... |
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¨ isFree... | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
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_ (... |
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
(Fo... | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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 f... | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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) [])
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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) [])
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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)) | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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_ ... | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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’ I... | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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)) | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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)) | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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_) | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
β’ IsProof ((forall_ v P).iff_ (exists_ v P.not_).not_)
TACTIC:
|
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)... | Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
v : VarName
β’ IsProof ((forall_ v P).iff_ (forall_ v P.not_.not_).not_.not_)
TACTIC:
|
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))) | Please generate a tactic in lean4 to solve the state.
STATE:
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_)
TACTIC:
|
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_).no... | Please generate a tactic in lean4 to solve the state.
STATE:
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_.n... |
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_).no... | 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_) | Please generate a tactic in lean4 to solve the state.
STATE:
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_
((... |
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_
((foral... | Please generate a tactic in lean4 to solve the state.
STATE:
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_
((foral... |
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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_)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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_
TACTIC:
|
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_) | Please generate a tactic in lean4 to solve the state.
STATE:
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_
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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_)
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_
TACTIC:
|
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)) | Please generate a tactic in lean4 to solve the state.
STATE:
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_
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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_
TACTIC:
|
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_) | Please generate a tactic in lean4 to solve the state.
STATE:
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_
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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_)
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ P P.not_.not_
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P = P
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a.a.a.a
P : Formula
v : VarName
β’ P.not_.not_ = P.not_.not_
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a
P : Formula
v : VarName
β’ IsReplOfFormulaInFormula P P.not_.not_ (forall_ v P) (forall_ v P)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a.a
P : Formula
v : VarName
β’ forall_ v P = forall_ v P
TACTIC:
|
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)) | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
P : Formula
v : VarName
β’ IsProof (P.iff_ P.not_.not_)
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).and_ (P.not_.not_.imp_ P))
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case h2
P : Formula
v : VarName
β’ IsProof ((P.imp_ P.not_.not_).imp_ (P.not_.not_.imp_ P).not_).not_
TACTIC:
|
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))) | Please generate a tactic in lean4 to solve the state.
STATE:
case h3
P : Formula
v : VarName
β’ IsDeduct β
((forall_ v P).iff_ (forall_ v P).not_.not_)
TACTIC:
|
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_ | Please generate a tactic in lean4 to solve the state.
STATE:
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)))
TACTIC:
|
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