url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
| input
stringlengths 73
2.09M
|
|---|---|---|---|---|---|---|---|---|---|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.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
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
h1 : IsProof P
Δ : Set Formula
s1 : IsDeduct Δ P
⊢ IsDeduct Δ P
TACTIC:
|
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✝)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1 : IsDeduct (Δ ∪ {P}) Q
⊢ IsDeduct Δ (P.imp_ Q)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ h1_phi
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom h1_phi
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ ∪ {P}
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P ∨ h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi = P
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsDeduct Δ (h1_phi.imp_ h1_phi)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
Q : Formula
Δ : Set Formula
h1_phi : Formula
⊢ IsProof (h1_phi.imp_ h1_phi)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ (P.imp_ h1_phi)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ IsDeduct Δ h1_phi
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P Q : Formula
Δ : Set Formula
h1_phi : Formula
h1_1 : h1_phi ∈ Δ
⊢ h1_phi ∈ Δ
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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)))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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)))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
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)))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
⊢ IsProof (P.not_.imp_ (P.imp_ Q))
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
⊢ IsDeduct ∅ (P.not_.imp_ (P.imp_ Q))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.imp_ Q)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
⊢ IsAxiom ((Q.not_.imp_ P.not_).imp_ (P.imp_ Q))
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (Q.not_.imp_ P.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) (P.not_.imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
⊢ IsAxiom (P.not_.imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.not_}) P.not_
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P Q : Formula
⊢ P.not_ ∈ ∅ ∪ {P.not_}
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof (P.not_.not_.imp_ P)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsDeduct ∅ (P.not_.not_.imp_ P)
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ P)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P : Formula
⊢ IsAxiom ((P.not_.imp_ P.not_.not_.not_).imp_ (P.not_.not_.imp_ P))
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.imp_ P.not_.not_.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.h1
P : Formula
⊢ IsProof (P.not_.not_.imp_ (P.not_.imp_ P.not_.not_.not_))
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_}
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P : Formula
⊢ IsDeduct (∅ ∪ {P.not_.not_}) P.not_.not_
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.not_.not_}
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsProof (P.imp_ P.not_.not_)
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P : Formula
⊢ IsDeduct ∅ (P.imp_ P.not_.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
⊢ IsDeduct ∅ ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.a
P : Formula
⊢ IsAxiom ((P.not_.not_.not_.imp_ P.not_).imp_ (P.imp_ P.not_.not_))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a
P : Formula
⊢ IsDeduct ∅ (P.not_.not_.not_.imp_ P.not_)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case a.h1
P : Formula
⊢ IsProof (P.not_.not_.not_.imp_ P.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
⊢ IsProof ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P Q : Formula
⊢ IsDeduct ∅ ((P.imp_ Q).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (Q.not_.imp_ P.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P Q : Formula
⊢ IsAxiom ((P.not_.not_.imp_ Q.not_.not_).imp_ (Q.not_.imp_ P.not_))
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q}) (P.not_.not_.imp_ Q.not_.not_)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q.not_.not_
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (Q.imp_ Q.not_.not_)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.h1
P Q : Formula
⊢ IsProof (Q.imp_ Q.not_.not_)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) Q
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.imp_ Q)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a
P Q : Formula
⊢ P.imp_ Q ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) (P.not_.not_.imp_ P)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.h1
P Q : Formula
⊢ IsProof (P.not_.not_.imp_ P)
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a
P Q : Formula
⊢ IsDeduct (∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}) P.not_.not_
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.a
P Q : Formula
⊢ P.not_.not_ ∈ ∅ ∪ {P.imp_ Q} ∪ {P.not_.not_}
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q R : Formula
⊢ IsProof (Q.imp_ (R.not_.imp_ (Q.imp_ R).not_))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
Q R : Formula
⊢ IsDeduct ∅ (Q.imp_ (R.not_.imp_ (Q.imp_ R).not_))
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (R.not_.imp_ (Q.imp_ R).not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
Q R : Formula
⊢ IsProof (((Q.imp_ R).imp_ R).imp_ (R.not_.imp_ (Q.imp_ R).not_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q}) ((Q.imp_ R).imp_ R)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) R
TACTIC:
|
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}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) (Q.imp_ R)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a
Q R : Formula
⊢ Q.imp_ R ∈ ∅ ∪ {Q} ∪ {Q.imp_ R}
TACTIC:
|
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}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
Q R : Formula
⊢ IsDeduct (∅ ∪ {Q} ∪ {Q.imp_ R}) Q
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a
Q R : Formula
⊢ Q ∈ ∅ ∪ {Q} ∪ {Q.imp_ R}
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
P S : Formula
⊢ IsProof ((S.imp_ P).imp_ ((S.not_.imp_ P).imp_ P))
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
P S : Formula
⊢ IsDeduct ∅ ((S.imp_ P).imp_ ((S.not_.imp_ P).imp_ P))
TACTIC:
|
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_)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) ((S.not_.imp_ P).imp_ P)
TACTIC:
|
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))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.a
P S : Formula
⊢ IsAxiom ((P.not_.imp_ (S.not_.imp_ P).not_).imp_ ((S.not_.imp_ P).imp_ P))
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P}) (P.not_.imp_ (S.not_.imp_ P).not_)
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.not_.imp_ P).not_
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ (S.not_.imp_ P).not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.h1
P S : Formula
⊢ IsProof (S.not_.imp_ (P.not_.imp_ (S.not_.imp_ P).not_))
TACTIC:
|
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_
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) S.not_
TACTIC:
|
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)
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (P.not_.imp_ S.not_)
TACTIC:
|
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_))
|
Please generate a tactic in lean4 to solve the state.
STATE:
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_))
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.a.h1
P S : Formula
⊢ IsProof ((S.imp_ P).imp_ (P.not_.imp_ S.not_))
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) (S.imp_ P)
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.a.a
P S : Formula
⊢ S.imp_ P ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_}
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_
TACTIC:
|
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
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a.a.a.a
P S : Formula
⊢ P.not_ ∈ ∅ ∪ {S.imp_ P} ∪ {P.not_}
TACTIC:
|
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_}
|
Please generate a tactic in lean4 to solve the state.
STATE:
case h1.a.h1.a
P S : Formula
⊢ IsDeduct (∅ ∪ {S.imp_ P} ∪ {P.not_}) P.not_
TACTIC:
|
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