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https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_11 | [319, 1] | [327, 11] | exact s1 | P : Formula
h1 : IsProof P
Δ : Set Formula
s1 : IsDeduct Δ P
⊢ IsDeduct Δ P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | induction h1 | P Q : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {P}) Q
⊢ IsDeduct Δ (P.imp_ Q) | case axiom_
P Q : Formula
Δ : Set Formula
phi✝ : Formula
a✝ : IsAxiom phi✝
⊢ IsDeduct Δ (P.imp_ phi✝)
case assume_
P Q : Formula
Δ : Set Formula
phi✝ : Formula
a✝ : phi✝ ∈ Δ ∪ {P}
⊢ IsDeduct Δ (P.imp_ phi✝)
case mp_
P Q : Formula
Δ : Set Formula
phi✝ psi✝ : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (phi✝.imp_ psi✝)
a✝ : IsDeduct (Δ ∪ {P}) phi✝
a_ih✝¹ : IsDeduct Δ (P.imp_ (phi✝.imp_ psi✝))
a_ih✝ : IsDeduct Δ (P.imp_ phi✝)
⊢ IsDeduct Δ (P.imp_ psi✝) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.mp_ h1_phi | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ (P.imp_ h1_phi) | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi))
case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ h1_phi |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.axiom_ | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact IsAxiom.prop_1_ h1_phi P | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.axiom_ | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ h1_phi | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom h1_phi |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact h1_1 | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom h1_phi | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | simp at h1_1 | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ ∪ {P}
⊢ IsDeduct Δ (P.imp_ h1_phi) | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P ∨ h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | cases h1_1 | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P ∨ h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi) | case inl
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h✝ : h1_phi = P
⊢ IsDeduct Δ (P.imp_ h1_phi)
case inr
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h✝ : h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | case inl h1_1 =>
subst h1_1
apply proof_imp_deduct
exact prop_id h1_phi | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P
⊢ IsDeduct Δ (P.imp_ h1_phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | subst h1_1 | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P
⊢ IsDeduct Δ (P.imp_ h1_phi) | Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsDeduct Δ (h1_phi.imp_ h1_phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply proof_imp_deduct | Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsDeduct Δ (h1_phi.imp_ h1_phi) | case h1
Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsProof (h1_phi.imp_ h1_phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact prop_id h1_phi | case h1
Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsProof (h1_phi.imp_ h1_phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.mp_ h1_phi | P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi) | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi))
case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ h1_phi |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.axiom_ | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ (h1_phi.imp_ (P.imp_ h1_phi)) | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact IsAxiom.prop_1_ h1_phi P | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsAxiom (h1_phi.imp_ (P.imp_ h1_phi)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.assume_ | case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ h1_phi | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ h1_phi ∈ Δ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact h1_1 | case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ h1_phi ∈ Δ | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.mp_ (P.imp_ h1_phi) | P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ (P.imp_ h1_psi) | case a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi))
case a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ (P.imp_ h1_phi) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.mp_ (P.imp_ (h1_phi.imp_ h1_psi)) | case a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi)) | case a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ ((P.imp_ (h1_phi.imp_ h1_psi)).imp_ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi)))
case a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | apply IsDeduct.axiom_ | case a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ ((P.imp_ (h1_phi.imp_ h1_psi)).imp_ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi))) | case a.a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsAxiom ((P.imp_ (h1_phi.imp_ h1_psi)).imp_ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi))) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact IsAxiom.prop_2_ P h1_phi h1_psi | case a.a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsAxiom ((P.imp_ (h1_phi.imp_ h1_psi)).imp_ ((P.imp_ h1_phi).imp_ (P.imp_ h1_psi))) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact h1_ih_1 | case a.a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_3 | [333, 1] | [366, 20] | exact h1_ih_2 | case a
P Q : Formula
Δ : Set Formula
h1_phi h1_psi : Formula
a✝¹ : IsDeduct (Δ ∪ {P}) (h1_phi.imp_ h1_psi)
a✝ : IsDeduct (Δ ∪ {P}) h1_phi
h1_ih_1 : IsDeduct Δ (P.imp_ (h1_phi.imp_ h1_psi))
h1_ih_2 : IsDeduct Δ (P.imp_ h1_phi)
⊢ IsDeduct Δ (P.imp_ h1_phi) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | simp only [IsProof] | P Q : Formula
⊢ IsProof (P.not_.imp_ (P.imp_ Q)) | P Q : Formula
⊢ IsDeduct ∅ (P.not_.imp_ (P.imp_ Q)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply deduction_theorem | P Q : Formula
⊢ IsDeduct ∅ (P.not_.imp_ (P.imp_ Q)) | case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.imp_ Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply IsDeduct.mp_ (Q.not_.imp_ P.not_) | case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.imp_ Q) | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (Q.not_.imp_ P.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply IsDeduct.axiom_ | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)) | case h1.a.a
P Q : Formula
⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | exact IsAxiom.prop_3_ Q P | case h1.a.a
P Q : Formula
⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply IsDeduct.mp_ P.not_ | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (Q.not_.imp_ P.not_) | case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.not_.imp_ (Q.not_.imp_ P.not_))
case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) P.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply IsDeduct.axiom_ | case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.not_.imp_ (Q.not_.imp_ P.not_)) | case h1.a.a.a
P Q : Formula
⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | exact IsAxiom.prop_1_ P.not_ Q.not_ | case h1.a.a.a
P Q : Formula
⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | apply IsDeduct.assume_ | case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) P.not_ | case h1.a.a.a
P Q : Formula
⊢ P.not_ ∈ ∅ ∪ {P.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_13_6 | [371, 1] | [384, 11] | simp | case h1.a.a.a
P Q : Formula
⊢ P.not_ ∈ ∅ ∪ {P.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | simp only [IsProof] | P : Formula
⊢ IsProof (P.not_.not_.imp_ P) | P : Formula
⊢ IsDeduct ∅ (P.not_.not_.imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply deduction_theorem | P : Formula
⊢ IsDeduct ∅ (P.not_.not_.imp_ P) | case h1
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.mp_ P.not_.not_ | case h1
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P | case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ P)
case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.mp_ (P.not_.imp_ P.not_.not_.not_) | case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ P) | case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P))
case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.imp_ P.not_.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.axiom_ | case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P)) | case h1.a.a.a
P : Formula
⊢ IsAxiom ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsAxiom.prop_3_ | case h1.a.a.a
P : Formula
⊢ IsAxiom ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.mp_ P.not_.not_ | case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.imp_ P.not_.not_.not_) | case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_))
case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply proof_imp_deduct | case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_)) | case h1.a.a.a.h1
P : Formula
⊢ IsProof (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply T_13_6 | case h1.a.a.a.h1
P : Formula
⊢ IsProof (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.assume_ | case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_ | case h1.a.a.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | simp | case h1.a.a.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | apply IsDeduct.assume_ | case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_ | case h1.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_5 | [387, 1] | [403, 9] | simp | case h1.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | simp only [IsProof] | P : Formula
⊢ IsProof (P.imp_ P.not_.not_) | P : Formula
⊢ IsDeduct ∅ (P.imp_ P.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | apply IsDeduct.mp_ (P.not_.not_.not_.imp_ P.not_) | P : Formula
⊢ IsDeduct ∅ (P.imp_ P.not_.not_) | case a
P : Formula
⊢ IsDeduct ∅ ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_))
case a
P : Formula
⊢ IsDeduct ∅ (P.not_.not_.not_.imp_ P.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | apply IsDeduct.axiom_ | case a
P : Formula
⊢ IsDeduct ∅ ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_)) | case a.a
P : Formula
⊢ IsAxiom ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | exact IsAxiom.prop_3_ P.not_.not_ P | case a.a
P : Formula
⊢ IsAxiom ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | apply proof_imp_deduct | case a
P : Formula
⊢ IsDeduct ∅ (P.not_.not_.not_.imp_ P.not_) | case a.h1
P : Formula
⊢ IsProof (P.not_.not_.not_.imp_ P.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_6 | [406, 1] | [415, 24] | exact T_14_5 P.not_ | case a.h1
P : Formula
⊢ IsProof (P.not_.not_.not_.imp_ P.not_) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | simp only [IsProof] | P Q : Formula
⊢ IsProof ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_)) | P Q : Formula
⊢ IsDeduct ∅ ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply deduction_theorem | P Q : Formula
⊢ IsDeduct ∅ ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_)) | case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (Q.not_.imp_ P.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.mp_ (P.not_.not_.imp_ Q.not_.not_) | case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (Q.not_.imp_ P.not_) | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_))
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (P.not_.not_.imp_ Q.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.axiom_ | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_)) | case h1.a.a
P Q : Formula
⊢ IsAxiom ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsAxiom.prop_3_ | case h1.a.a
P Q : Formula
⊢ IsAxiom ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply deduction_theorem | case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (P.not_.not_.imp_ Q.not_.not_) | case h1.a.h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.mp_ Q | case h1.a.h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q.not_.not_ | case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (Q.imp_ Q.not_.not_)
case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply proof_imp_deduct | case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (Q.imp_ Q.not_.not_) | case h1.a.h1.a.h1
P Q : Formula
⊢ IsProof (Q.imp_ Q.not_.not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply T_14_6 | case h1.a.h1.a.h1
P Q : Formula
⊢ IsProof (Q.imp_ Q.not_.not_) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.mp_ P | case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q | case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.imp_ Q)
case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.assume_ | case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.imp_ Q) | case h1.a.h1.a.a.a
P Q : Formula
⊢ P.imp_ Q ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | simp | case h1.a.h1.a.a.a
P Q : Formula
⊢ P.imp_ Q ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.mp_ P.not_.not_ | case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P | case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.not_.not_.imp_ P)
case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P.not_.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply proof_imp_deduct | case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.not_.not_.imp_ P) | case h1.a.h1.a.a.a.h1
P Q : Formula
⊢ IsProof (P.not_.not_.imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply T_14_5 | case h1.a.h1.a.a.a.h1
P Q : Formula
⊢ IsProof (P.not_.not_.imp_ P) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | apply IsDeduct.assume_ | case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P.not_.not_ | case h1.a.h1.a.a.a.a
P Q : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_7 | [418, 1] | [438, 15] | simp | case h1.a.h1.a.a.a.a
P Q : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | simp only [IsProof] | Q R : Formula
⊢ IsProof (Q.imp_ (R.not_.imp_ (Q.imp_ R).not_)) | Q R : Formula
⊢ IsDeduct ∅ (Q.imp_ (R.not_.imp_ (Q.imp_ R).not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply deduction_theorem | Q R : Formula
⊢ IsDeduct ∅ (Q.imp_ (R.not_.imp_ (Q.imp_ R).not_)) | case h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (R.not_.imp_ (Q.imp_ R).not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply IsDeduct.mp_ ((Q.imp_ R).imp_ R) | case h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (R.not_.imp_ (Q.imp_ R).not_) | case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_))
case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) ((Q.imp_ R).imp_ R) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply proof_imp_deduct | case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_)) | case h1.a.h1
Q R : Formula
⊢ IsProof (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply T_14_7 | case h1.a.h1
Q R : Formula
⊢ IsProof (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply deduction_theorem | case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) ((Q.imp_ R).imp_ R) | case h1.a.h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) R |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply IsDeduct.mp_ Q | case h1.a.h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) R | case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) (Q.imp_ R)
case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) Q |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply IsDeduct.assume_ | case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) (Q.imp_ R) | case h1.a.h1.a.a
Q R : Formula
⊢ Q.imp_ R ∈ ∅ ∪ {Q} ∪ {Q.imp_ R} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | simp | case h1.a.h1.a.a
Q R : Formula
⊢ Q.imp_ R ∈ ∅ ∪ {Q} ∪ {Q.imp_ R} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | apply IsDeduct.assume_ | case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) Q | case h1.a.h1.a.a
Q R : Formula
⊢ Q ∈ ∅ ∪ {Q} ∪ {Q.imp_ R} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_8 | [441, 1] | [455, 11] | simp | case h1.a.h1.a.a
Q R : Formula
⊢ Q ∈ ∅ ∪ {Q} ∪ {Q.imp_ R} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | simp only [IsProof] | P S : Formula
⊢ IsProof ((S.imp_ P).imp_ ((S.not_.imp_ P).imp_ P)) | P S : Formula
⊢ IsDeduct ∅ ((S.imp_ P).imp_ ((S.not_.imp_ P).imp_ P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply deduction_theorem | P S : Formula
⊢ IsDeduct ∅ ((S.imp_ P).imp_ ((S.not_.imp_ P).imp_ P)) | case h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) ((S.not_.imp_ P).imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.mp_ (P.not_.imp_ (S.not_.imp_ P).not_) | case h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) ((S.not_.imp_ P).imp_ P) | case h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) ((P.not_.imp_ (S.not_.imp_ P).not_).imp_ ((S.not_.imp_ P).imp_ P))
case h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) (P.not_.imp_ (S.not_.imp_ P).not_) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.axiom_ | case h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) ((P.not_.imp_ (S.not_.imp_ P).not_).imp_ ((S.not_.imp_ P).imp_ P)) | case h1.a.a
P S : Formula
⊢ IsAxiom ((P.not_.imp_ (S.not_.imp_ P).not_).imp_ ((S.not_.imp_ P).imp_ P)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsAxiom.prop_3_ | case h1.a.a
P S : Formula
⊢ IsAxiom ((P.not_.imp_ (S.not_.imp_ P).not_).imp_ ((S.not_.imp_ P).imp_ P)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply deduction_theorem | case h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) (P.not_.imp_ (S.not_.imp_ P).not_) | case h1.a.h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.not_.imp_ P).not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.mp_ P.not_ | case h1.a.h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.not_.imp_ P).not_ | case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ (S.not_.imp_ P).not_)
case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.mp_ S.not_ | case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ (S.not_.imp_ P).not_) | case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.not_.imp_ (P.not_.imp_ (S.not_.imp_ P).not_))
case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) S.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply proof_imp_deduct | case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.not_.imp_ (P.not_.imp_ (S.not_.imp_ P).not_)) | case h1.a.h1.a.a.h1
P S : Formula
⊢ IsProof (S.not_.imp_ (P.not_.imp_ (S.not_.imp_ P).not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply T_14_8 | case h1.a.h1.a.a.h1
P S : Formula
⊢ IsProof (S.not_.imp_ (P.not_.imp_ (S.not_.imp_ P).not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.mp_ P.not_ | case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) S.not_ | case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ S.not_)
case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_ |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.mp_ (S.imp_ P) | case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ S.not_) | case h1.a.h1.a.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) ((S.imp_ P).imp_ (P.not_.imp_ S.not_))
case h1.a.h1.a.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.imp_ P) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply proof_imp_deduct | case h1.a.h1.a.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) ((S.imp_ P).imp_ (P.not_.imp_ S.not_)) | case h1.a.h1.a.a.a.a.h1
P S : Formula
⊢ IsProof ((S.imp_ P).imp_ (P.not_.imp_ S.not_)) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply T_14_7 | case h1.a.h1.a.a.a.a.h1
P S : Formula
⊢ IsProof ((S.imp_ P).imp_ (P.not_.imp_ S.not_)) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.assume_ | case h1.a.h1.a.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.imp_ P) | case h1.a.h1.a.a.a.a.a
P S : Formula
⊢ S.imp_ P ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | simp | case h1.a.h1.a.a.a.a.a
P S : Formula
⊢ S.imp_ P ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.assume_ | case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_ | case h1.a.h1.a.a.a.a
P S : Formula
⊢ P.not_ ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | simp | case h1.a.h1.a.a.a.a
P S : Formula
⊢ P.not_ ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_9 | [458, 1] | [481, 11] | apply IsDeduct.assume_ | case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_ | case h1.a.h1.a.a
P S : Formula
⊢ P.not_ ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_} |
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