url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/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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