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/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
case axiom_ h1_phi h1_1 =>
apply IsDeduct.axiom_
exact h1_1
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsDeduct Ξ h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsDeduct Ξ h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
case assume_ h1_phi h1_1 => exact h2 h1_phi h1_1
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : h1_phi β Ξ
β’ IsDeduct Ξ h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : h1_phi β Ξ
β’ IsDeduct Ξ h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
case mp_ h1_phi h1_psi _ _ h1_ih_1 h1_ih_2 =>
exact IsDeduct.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi h1_psi : Formula
aβΒΉ : IsDeduct Ξ (h1_phi.imp_ h1_psi)
aβ : IsDeduct Ξ h1_phi
h1_ih_1 : IsDeduct Ξ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Ξ h1_phi
β’ IsDeduct Ξ h1_psi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi h1_psi : Formula
aβΒΉ : IsDeduct Ξ (h1_phi.imp_ h1_psi)
aβ : IsDeduct Ξ h1_phi
h1_ih_1 : IsDeduct Ξ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Ξ h1_phi
β’ IsDeduct Ξ h1_psi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
apply IsDeduct.axiom_
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsDeduct Ξ h1_phi
|
case a
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsAxiom h1_phi
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsDeduct Ξ h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact h1_1
|
case a
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsAxiom h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
β’ IsAxiom h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact h2 h1_phi h1_1
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : h1_phi β Ξ
β’ IsDeduct Ξ h1_phi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi : Formula
h1_1 : h1_phi β Ξ
β’ IsDeduct Ξ h1_phi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact IsDeduct.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi h1_psi : Formula
aβΒΉ : IsDeduct Ξ (h1_phi.imp_ h1_psi)
aβ : IsDeduct Ξ h1_phi
h1_ih_1 : IsDeduct Ξ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Ξ h1_phi
β’ IsDeduct Ξ h1_psi
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ Ξ : Set Formula
h2 : β H β Ξ, IsDeduct Ξ H
h1_phi h1_psi : Formula
aβΒΉ : IsDeduct Ξ (h1_phi.imp_ h1_psi)
aβ : IsDeduct Ξ h1_phi
h1_ih_1 : IsDeduct Ξ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Ξ h1_phi
β’ IsDeduct Ξ h1_psi
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
simp only [IsProof] at h2
|
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsProof P
β’ IsProof Q
|
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsProof Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsProof P
β’ IsProof Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
simp only [IsProof]
|
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsProof Q
|
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsDeduct β
Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsProof Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
exact T_14_16 Q β
Ξ h1 h2
|
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsDeduct β
Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q : Formula
Ξ : Set Formula
h1 : IsDeduct Ξ Q
h2 : β P β Ξ, IsDeduct β
P
β’ IsDeduct β
Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_not
|
[566, 1]
|
[572, 32]
|
simp only [Formula.evalPrime]
|
P : Formula
V : VarBoolAssignment
β’ evalPrime V P.not_ β Β¬evalPrime V P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
V : VarBoolAssignment
β’ evalPrime V P.not_ β Β¬evalPrime V P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_imp
|
[575, 1]
|
[581, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.imp_ Q) β evalPrime V P β evalPrime V Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.imp_ Q) β evalPrime V P β evalPrime V Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_false
|
[584, 1]
|
[589, 32]
|
simp only [Formula.evalPrime]
|
V : VarBoolAssignment
β’ evalPrime V false_ β False
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
V : VarBoolAssignment
β’ evalPrime V false_ β False
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_and
|
[592, 1]
|
[598, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.and_ Q) β evalPrime V P β§ evalPrime V Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.and_ Q) β evalPrime V P β§ evalPrime V Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_or
|
[601, 1]
|
[607, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.or_ Q) β evalPrime V P β¨ evalPrime V Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.or_ Q) β evalPrime V P β¨ evalPrime V Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_iff
|
[610, 1]
|
[616, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.iff_ Q) β (evalPrime V P β evalPrime V Q)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
V : VarBoolAssignment
β’ evalPrime V (P.iff_ Q) β (evalPrime V P β evalPrime V Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp only [Formula.IsTautoPrime]
|
β’ true_.IsTautoPrime
|
β’ β (V : VarBoolAssignment), evalPrime V true_
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ true_.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp only [Formula.evalPrime]
|
β’ β (V : VarBoolAssignment), evalPrime V true_
|
β’ VarBoolAssignment β True
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (V : VarBoolAssignment), evalPrime V true_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp
|
β’ VarBoolAssignment β True
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ VarBoolAssignment β True
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_1
|
[627, 1]
|
[632, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
β’ (P.imp_ (Q.imp_ P)).IsTautoPrime
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V (P.imp_ (Q.imp_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ (P.imp_ (Q.imp_ P)).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_1
|
[627, 1]
|
[632, 8]
|
tauto
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V (P.imp_ (Q.imp_ P))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V (P.imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_2
|
[635, 1]
|
[640, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q R : Formula
β’ ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R))).IsTautoPrime
|
P Q R : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q R : Formula
β’ ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R))).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_2
|
[635, 1]
|
[640, 8]
|
tauto
|
P Q R : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q R : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
β’ ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P)).IsTautoPrime
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P)).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
simp only [eval_not, eval_imp]
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P))
|
P Q : Formula
β’ β (V : VarBoolAssignment), (Β¬evalPrime V P β Β¬evalPrime V Q) β evalPrime V Q β evalPrime V P
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
tauto
|
P Q : Formula
β’ β (V : VarBoolAssignment), (Β¬evalPrime V P β Β¬evalPrime V Q) β evalPrime V Q β evalPrime V P
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), (Β¬evalPrime V P β Β¬evalPrime V Q) β evalPrime V Q β evalPrime V P
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [Formula.IsTautoPrime] at h1
|
P Q : Formula
h1 : (P.imp_ Q).IsTautoPrime
h2 : P.IsTautoPrime
β’ Q.IsTautoPrime
|
P Q : Formula
h1 : β (V : VarBoolAssignment), evalPrime V (P.imp_ Q)
h2 : P.IsTautoPrime
β’ Q.IsTautoPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
h1 : (P.imp_ Q).IsTautoPrime
h2 : P.IsTautoPrime
β’ Q.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [eval_imp] at h1
|
P Q : Formula
h1 : β (V : VarBoolAssignment), evalPrime V (P.imp_ Q)
h2 : P.IsTautoPrime
β’ Q.IsTautoPrime
|
P Q : Formula
h2 : P.IsTautoPrime
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
h1 : β (V : VarBoolAssignment), evalPrime V (P.imp_ Q)
h2 : P.IsTautoPrime
β’ Q.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [Formula.IsTautoPrime] at h2
|
P Q : Formula
h2 : P.IsTautoPrime
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
|
P Q : Formula
h2 : β (V : VarBoolAssignment), evalPrime V P
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
h2 : P.IsTautoPrime
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
tauto
|
P Q : Formula
h2 : β (V : VarBoolAssignment), evalPrime V P
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
h2 : β (V : VarBoolAssignment), evalPrime V P
h1 : β (V : VarBoolAssignment), evalPrime V P β evalPrime V Q
β’ Q.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
simp only [Formula.IsTautoPrime]
|
β’ (false_.iff_ true_.not_).IsTautoPrime
|
β’ β (V : VarBoolAssignment), evalPrime V (false_.iff_ true_.not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ (false_.iff_ true_.not_).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
simp only [eval_not, eval_iff]
|
β’ β (V : VarBoolAssignment), evalPrime V (false_.iff_ true_.not_)
|
β’ β (V : VarBoolAssignment), evalPrime V false_ β Β¬evalPrime V true_
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (V : VarBoolAssignment), evalPrime V (false_.iff_ true_.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
tauto
|
β’ β (V : VarBoolAssignment), evalPrime V false_ β Β¬evalPrime V true_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
β’ β (V : VarBoolAssignment), evalPrime V false_ β Β¬evalPrime V true_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
β’ ((P.and_ Q).iff_ (P.imp_ Q.not_).not_).IsTautoPrime
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.and_ Q).iff_ (P.imp_ Q.not_).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ ((P.and_ Q).iff_ (P.imp_ Q.not_).not_).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
simp only [eval_and, eval_not, eval_imp, eval_iff]
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.and_ Q).iff_ (P.imp_ Q.not_).not_)
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β§ evalPrime V Q β Β¬(evalPrime V P β Β¬evalPrime V Q)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.and_ Q).iff_ (P.imp_ Q.not_).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
tauto
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β§ evalPrime V Q β Β¬(evalPrime V P β Β¬evalPrime V Q)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β§ evalPrime V Q β Β¬(evalPrime V P β Β¬evalPrime V Q)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
β’ ((P.or_ Q).iff_ (P.not_.imp_ Q)).IsTautoPrime
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.or_ Q).iff_ (P.not_.imp_ Q))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ ((P.or_ Q).iff_ (P.not_.imp_ Q)).IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
simp only [eval_or, eval_not, eval_imp, eval_iff]
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.or_ Q).iff_ (P.not_.imp_ Q))
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β¨ evalPrime V Q β Β¬evalPrime V P β evalPrime V Q
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V ((P.or_ Q).iff_ (P.not_.imp_ Q))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
tauto
|
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β¨ evalPrime V Q β Β¬evalPrime V P β evalPrime V Q
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment), evalPrime V P β¨ evalPrime V Q β Β¬evalPrime V P β evalPrime V Q
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
β’ (((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_.IsTautoPrime
|
P Q : Formula
β’ β (V : VarBoolAssignment),
evalPrime V
(((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ (((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_.IsTautoPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
simp only [eval_iff, eval_not, eval_imp]
|
P Q : Formula
β’ β (V : VarBoolAssignment),
evalPrime V
(((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_
|
P Q : Formula
β’ β (V : VarBoolAssignment),
Β¬(((evalPrime V P β evalPrime V Q) β Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P))) β
Β¬(Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P)) β (evalPrime V P β evalPrime V Q)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment),
evalPrime V
(((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
tauto
|
P Q : Formula
β’ β (V : VarBoolAssignment),
Β¬(((evalPrime V P β evalPrime V Q) β Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P))) β
Β¬(Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P)) β (evalPrime V P β evalPrime V Q)))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
β’ β (V : VarBoolAssignment),
Β¬(((evalPrime V P β evalPrime V Q) β Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P))) β
Β¬(Β¬((evalPrime V P β evalPrime V Q) β Β¬(evalPrime V Q β evalPrime V P)) β (evalPrime V P β evalPrime V Q)))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
induction F
|
F F' : Formula
h1 : F' β F.primeSet
β’ F'.IsPrime
|
case pred_const_
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_const_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
case pred_var_
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_var_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
case eq_
F' : Formula
aβΒΉ aβ : VarName
h1 : F' β (eq_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
case true_
F' : Formula
h1 : F' β true_.primeSet
β’ F'.IsPrime
case false_
F' : Formula
h1 : F' β false_.primeSet
β’ F'.IsPrime
case not_
F' aβ : Formula
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β aβ.not_.primeSet
β’ F'.IsPrime
case imp_
F' aβΒΉ aβ : Formula
a_ihβΒΉ : F' β aβΒΉ.primeSet β F'.IsPrime
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (aβΒΉ.imp_ aβ).primeSet
β’ F'.IsPrime
case and_
F' aβΒΉ aβ : Formula
a_ihβΒΉ : F' β aβΒΉ.primeSet β F'.IsPrime
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (aβΒΉ.and_ aβ).primeSet
β’ F'.IsPrime
case or_
F' aβΒΉ aβ : Formula
a_ihβΒΉ : F' β aβΒΉ.primeSet β F'.IsPrime
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (aβΒΉ.or_ aβ).primeSet
β’ F'.IsPrime
case iff_
F' aβΒΉ aβ : Formula
a_ihβΒΉ : F' β aβΒΉ.primeSet β F'.IsPrime
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (aβΒΉ.iff_ aβ).primeSet
β’ F'.IsPrime
case forall_
F' : Formula
aβΒΉ : VarName
aβ : Formula
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (forall_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
case exists_
F' : Formula
aβΒΉ : VarName
aβ : Formula
a_ihβ : F' β aβ.primeSet β F'.IsPrime
h1 : F' β (exists_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
case def_
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β (def_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
h1 : F' β F.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case pred_const_ | pred_var_ =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_var_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_var_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case true_ | false_ =>
simp only [Formula.primeSet] at h1
simp at h1
|
F' : Formula
h1 : F' β false_.primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
h1 : F' β false_.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case eq_ x y =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
x y : VarName
h1 : F' β (eq_ x y).primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
x y : VarName
h1 : F' β (eq_ x y).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case not_ phi phi_ih =>
simp only [Formula.primeSet] at h1
exact phi_ih h1
|
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.not_.primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.not_.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case
imp_ phi psi phi_ih psi_ih
| and_ phi psi phi_ih psi_ih
| or_ phi psi phi_ih psi_ih
| iff_ phi psi phi_ih psi_ih =>
simp only [Formula.primeSet] at h1
simp at h1
tauto
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β (phi.iff_ psi).primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β (phi.iff_ psi).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case forall_ x phi | exists_ x phi =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β (exists_ aβ x).primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β (exists_ aβ x).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case def_ =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β (def_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β (def_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_var_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β {pred_var_ aβΒΉ aβ}
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β (pred_var_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β {pred_var_ aβΒΉ aβ}
β’ F'.IsPrime
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' = pred_var_ aβΒΉ aβ
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' β {pred_var_ aβΒΉ aβ}
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' = pred_var_ aβΒΉ aβ
β’ F'.IsPrime
|
aβΒΉ : PredName
aβ : List VarName
β’ (pred_var_ aβΒΉ aβ).IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : PredName
aβ : List VarName
h1 : F' = pred_var_ aβΒΉ aβ
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
aβΒΉ : PredName
aβ : List VarName
β’ (pred_var_ aβΒΉ aβ).IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
aβΒΉ : PredName
aβ : List VarName
β’ (pred_var_ aβΒΉ aβ).IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
h1 : F' β false_.primeSet
β’ F'.IsPrime
|
F' : Formula
h1 : F' β β
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
h1 : F' β false_.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
h1 : F' β β
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
h1 : F' β β
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
x y : VarName
h1 : F' β (eq_ x y).primeSet
β’ F'.IsPrime
|
F' : Formula
x y : VarName
h1 : F' β {eq_ x y}
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
x y : VarName
h1 : F' β (eq_ x y).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
x y : VarName
h1 : F' β {eq_ x y}
β’ F'.IsPrime
|
F' : Formula
x y : VarName
h1 : F' = eq_ x y
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
x y : VarName
h1 : F' β {eq_ x y}
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
x y : VarName
h1 : F' = eq_ x y
β’ F'.IsPrime
|
x y : VarName
β’ (eq_ x y).IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
x y : VarName
h1 : F' = eq_ x y
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
x y : VarName
β’ (eq_ x y).IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
x y : VarName
β’ (eq_ x y).IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.not_.primeSet
β’ F'.IsPrime
|
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.not_.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
exact phi_ih h1
|
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β (phi.iff_ psi).primeSet
β’ F'.IsPrime
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet βͺ psi.primeSet
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β (phi.iff_ psi).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet βͺ psi.primeSet
β’ F'.IsPrime
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet β¨ F' β psi.primeSet
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet βͺ psi.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
tauto
|
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet β¨ F' β psi.primeSet
β’ F'.IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' phi psi : Formula
phi_ih : F' β phi.primeSet β F'.IsPrime
psi_ih : F' β psi.primeSet β F'.IsPrime
h1 : F' β phi.primeSet β¨ F' β psi.primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β (exists_ aβ x).primeSet
β’ F'.IsPrime
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β {exists_ aβ x}
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β (exists_ aβ x).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β {exists_ aβ x}
β’ F'.IsPrime
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' = exists_ aβ x
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' β {exists_ aβ x}
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' = exists_ aβ x
β’ F'.IsPrime
|
aβ : VarName
x : Formula
phi : exists_ aβ x β x.primeSet β (exists_ aβ x).IsPrime
β’ (exists_ aβ x).IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβ : VarName
x : Formula
phi : F' β x.primeSet β F'.IsPrime
h1 : F' = exists_ aβ x
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
aβ : VarName
x : Formula
phi : exists_ aβ x β x.primeSet β (exists_ aβ x).IsPrime
β’ (exists_ aβ x).IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
aβ : VarName
x : Formula
phi : exists_ aβ x β x.primeSet β (exists_ aβ x).IsPrime
β’ (exists_ aβ x).IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β (def_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β {def_ aβΒΉ aβ}
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β (def_ aβΒΉ aβ).primeSet
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β {def_ aβΒΉ aβ}
β’ F'.IsPrime
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' = def_ aβΒΉ aβ
β’ F'.IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' β {def_ aβΒΉ aβ}
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' = def_ aβΒΉ aβ
β’ F'.IsPrime
|
aβΒΉ : DefName
aβ : List VarName
β’ (def_ aβΒΉ aβ).IsPrime
|
Please generate a tactic in lean4 to solve the state.
STATE:
F' : Formula
aβΒΉ : DefName
aβ : List VarName
h1 : F' = def_ aβΒΉ aβ
β’ F'.IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
aβΒΉ : DefName
aβ : List VarName
β’ (def_ aβΒΉ aβ).IsPrime
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
aβΒΉ : DefName
aβ : List VarName
β’ (def_ aβΒΉ aβ).IsPrime
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
subst h2
|
F F' : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
Ξ_U' : Set Formula
h1 : βF.primeSet β Ξ_U
h2 : Ξ_U' = evalPrimeFfToNot V '' Ξ_U
h3 : F' = evalPrimeFfToNot V F
β’ IsDeduct Ξ_U' F'
|
F F' : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
h3 : F' = evalPrimeFfToNot V F
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) F'
|
Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
Ξ_U' : Set Formula
h1 : βF.primeSet β Ξ_U
h2 : Ξ_U' = evalPrimeFfToNot V '' Ξ_U
h3 : F' = evalPrimeFfToNot V F
β’ IsDeduct Ξ_U' F'
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
subst h3
|
F F' : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
h3 : F' = evalPrimeFfToNot V F
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) F'
|
F : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V F)
|
Please generate a tactic in lean4 to solve the state.
STATE:
F F' : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
h3 : F' = evalPrimeFfToNot V F
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) F'
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
induction F
|
F : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V F)
|
case pred_const_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : PredName
aβ : List VarName
h1 : β(pred_const_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ aβΒΉ aβ))
case pred_var_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : PredName
aβ : List VarName
h1 : β(pred_var_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ aβΒΉ aβ))
case eq_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ aβ : VarName
h1 : β(eq_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (eq_ aβΒΉ aβ))
case true_
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βtrue_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V true_)
case false_
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βfalse_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V false_)
case not_
Ξ_U : Set Formula
V : VarBoolAssignment
aβ : Formula
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : βaβ.not_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ.not_)
case imp_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ aβ : Formula
a_ihβΒΉ : βaβΒΉ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβΒΉ)
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(aβΒΉ.imp_ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (aβΒΉ.imp_ aβ))
case and_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ aβ : Formula
a_ihβΒΉ : βaβΒΉ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβΒΉ)
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(aβΒΉ.and_ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (aβΒΉ.and_ aβ))
case or_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ aβ : Formula
a_ihβΒΉ : βaβΒΉ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβΒΉ)
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(aβΒΉ.or_ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (aβΒΉ.or_ aβ))
case iff_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ aβ : Formula
a_ihβΒΉ : βaβΒΉ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβΒΉ)
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(aβΒΉ.iff_ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (aβΒΉ.iff_ aβ))
case forall_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : VarName
aβ : Formula
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(forall_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (forall_ aβΒΉ aβ))
case exists_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : VarName
aβ : Formula
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(exists_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (exists_ aβΒΉ aβ))
case def_
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : DefName
aβ : List VarName
h1 : β(def_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (def_ aβΒΉ aβ))
|
Please generate a tactic in lean4 to solve the state.
STATE:
F : Formula
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βF.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V F)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case pred_const_ X xs =>
let F := pred_const_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case pred_var_ X xs =>
let F := pred_var_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case eq_ x y =>
let F := eq_ x y
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Ξ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : β(eq_ x y).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (eq_ x y))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : β(eq_ x y).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (eq_ x y))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case true_ =>
apply IsDeduct.axiom_
apply IsAxiom.prop_true_
|
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βtrue_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V true_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βtrue_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V true_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case false_ =>
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
simp
sorry
|
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βfalse_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V false_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
h1 : βfalse_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V false_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case not_ phi phi_ih =>
simp only [Formula.primeSet] at h1
simp only [evalPrimeFfToNot] at phi_ih
simp only [evalPrimeFfToNot]
simp only [evalPrime]
simp
split_ifs
case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
apply IsDeduct.mp_ phi
apply proof_imp_deduct
apply T_14_6
exact phi_ih h1
case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
exact phi_ih h1
|
Ξ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : βphi.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi)
h1 : βphi.not_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi.not_)
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : βphi.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi)
h1 : βphi.not_.primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi.not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case forall_ x phi phi_ih =>
let F := forall_ x phi
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Ξ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : βphi.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi)
h1 : β(forall_ x phi).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (forall_ x phi))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : βphi.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V phi)
h1 : β(forall_ x phi).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (forall_ x phi))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case def_ X xs =>
let F := def_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : β(def_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (def_ X xs))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : β(def_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (def_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case and_ | or_ | iff_ | exists_ =>
sorry
|
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : VarName
aβ : Formula
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(exists_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (exists_ aβΒΉ aβ))
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
aβΒΉ : VarName
aβ : Formula
a_ihβ : βaβ.primeSet β Ξ_U β IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V aβ)
h1 : β(exists_ aβΒΉ aβ).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (exists_ aβΒΉ aβ))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
let F := pred_const_ X xs
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.primeSet] at h1
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_const_ X xs} β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_const_ X xs).primeSet β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp at h1
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_const_ X xs} β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_const_ X xs} β Ξ_U
F : Formula := pred_const_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [evalPrimeFfToNot]
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_const_ X xs) then pred_const_ X xs else (pred_const_ X xs).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_const_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.evalPrime]
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_const_ X xs) then pred_const_ X xs else (pred_const_ X xs).not_)
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_const_ X xs) then pred_const_ X xs else (pred_const_ X xs).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply IsDeduct.assume_
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_)
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ (if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_) β
(fun a => if evalPrime V a then a else a.not_) '' Ξ_U
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ (if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_) β
(fun a => if evalPrime V a then a else a.not_) '' Ξ_U
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ β x β Ξ_U,
(if evalPrime V x then x else x.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ (if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_) β
(fun a => if evalPrime V a then a else a.not_) '' Ξ_U
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply Exists.intro F
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ β x β Ξ_U,
(if evalPrime V x then x else x.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ F β Ξ_U β§
(if evalPrime V F then F else F.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ β x β Ξ_U,
(if evalPrime V x then x else x.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
tauto
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ F β Ξ_U β§
(if evalPrime V F then F else F.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
no goals
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs β Ξ_U
β’ F β Ξ_U β§
(if evalPrime V F then F else F.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
let F := pred_var_ X xs
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.primeSet] at h1
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_var_ X xs} β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β(pred_var_ X xs).primeSet β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp at h1
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_var_ X xs} β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : β{pred_var_ X xs} β Ξ_U
F : Formula := pred_var_ X xs
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [evalPrimeFfToNot]
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_var_ X xs) then pred_var_ X xs else (pred_var_ X xs).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct (evalPrimeFfToNot V '' Ξ_U) (evalPrimeFfToNot V (pred_var_ X xs))
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.evalPrime]
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_var_ X xs) then pred_var_ X xs else (pred_var_ X xs).not_)
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if evalPrime V (pred_var_ X xs) then pred_var_ X xs else (pred_var_ X xs).not_)
TACTIC:
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply IsDeduct.assume_
|
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_)
|
case a
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ (if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_) β
(fun a => if evalPrime V a then a else a.not_) '' Ξ_U
|
Please generate a tactic in lean4 to solve the state.
STATE:
Ξ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs β Ξ_U
β’ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Ξ_U)
(if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_)
TACTIC:
|
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