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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_} |
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
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.deductionTheoremConverse | [484, 1] | [493, 9] | apply IsDeduct.mp_ P | P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ {P}) Q | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ {P}) (P.imp_ Q)
case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ {P}) P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.deductionTheoremConverse | [484, 1] | [493, 9] | exact T_14_10 (P.imp_ Q) Δ h1 {P} | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ {P}) (P.imp_ Q) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.deductionTheoremConverse | [484, 1] | [493, 9] | apply IsDeduct.assume_ | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ {P}) P | case a.a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ P ∈ Δ ∪ {P} |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.deductionTheoremConverse | [484, 1] | [493, 9] | simp | case a.a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ (P.imp_ Q)
⊢ P ∈ Δ ∪ {P} | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_12 | [496, 1] | [506, 13] | apply IsDeduct.mp_ P | P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ Γ) Q | case a
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ Γ) (P.imp_ Q)
case a
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ Γ) P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_12 | [496, 1] | [506, 13] | apply T_14_10_comm | case a
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ Γ) (P.imp_ Q) | case a.h1
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ (P.imp_ Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_12 | [496, 1] | [506, 13] | exact h2 | case a.h1
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ (P.imp_ Q) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_12 | [496, 1] | [506, 13] | apply T_14_10 | case a
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct (Δ ∪ Γ) P | case a.h1
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Δ P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_12 | [496, 1] | [506, 13] | exact h1 | case a.h1
P Q : Formula
Δ Γ : Set Formula
h1 : IsDeduct Δ P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Δ P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_14 | [509, 1] | [518, 13] | apply IsDeduct.mp_ P | P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ Q | case a
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ (P.imp_ Q)
case a
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_14 | [509, 1] | [518, 13] | exact h2 | case a
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ (P.imp_ Q) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_14 | [509, 1] | [518, 13] | apply proof_imp_deduct | case a
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsDeduct Γ P | case a.h1
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsProof P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_14 | [509, 1] | [518, 13] | exact h1 | case a.h1
P Q : Formula
Γ : Set Formula
h1 : IsProof P
h2 : IsDeduct Γ (P.imp_ Q)
⊢ IsProof P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_15 | [523, 1] | [532, 13] | apply IsDeduct.mp_ P | P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ Q | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ (P.imp_ Q)
case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ P |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_15 | [523, 1] | [532, 13] | apply proof_imp_deduct | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ (P.imp_ Q) | case a.h1
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsProof (P.imp_ Q) |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_15 | [523, 1] | [532, 13] | exact h2 | case a.h1
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsProof (P.imp_ Q) | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.C_14_15 | [523, 1] | [532, 13] | exact h1 | case a
P Q : Formula
Δ : Set Formula
h1 : IsDeduct Δ P
h2 : IsProof (P.imp_ Q)
⊢ IsDeduct Δ P | no goals |
https://github.com/pthomas505/FOL.git | 097a4abea51b641d144539b9a0f7516f3b9d818c | FOL/NV/Margaris/Prop.lean | FOL.NV.T_14_16 | [537, 1] | [550, 53] | induction h1 | F : Formula
Δ Γ : Set Formula
h1 : IsDeduct Γ F
h2 : ∀ H ∈ Γ, IsDeduct Δ H
⊢ IsDeduct Δ F | case axiom_
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
phi✝ : Formula
a✝ : IsAxiom phi✝
⊢ IsDeduct Δ phi✝
case assume_
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
phi✝ : Formula
a✝ : phi✝ ∈ Γ
⊢ IsDeduct Δ phi✝
case mp_
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
phi✝ psi✝ : Formula
a✝¹ : IsDeduct Γ (phi✝.imp_ psi✝)
a✝ : IsDeduct Γ phi✝
a_ih✝¹ : IsDeduct Δ (phi✝.imp_ psi✝)
a_ih✝ : IsDeduct Δ phi✝
⊢ IsDeduct Δ psi✝ |
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