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_16
|
[537, 1]
|
[550, 53]
|
case axiom_ h1_phi h1_1 =>
apply IsDeduct.axiom_
exact h1_1
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ h1_phi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
case assume_ h1_phi h1_1 => exact h2 h1_phi h1_1
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : h1_phi ∈ Γ
⊢ IsDeduct Δ h1_phi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
case mp_ h1_phi h1_psi _ _ h1_ih_1 h1_ih_2 =>
exact IsDeduct.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi h1_psi : Formula
a✝¹ : IsDeduct Γ (h1_phi.imp_ h1_psi)
a✝ : IsDeduct Γ h1_phi
h1_ih_1 : IsDeduct Δ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Δ h1_phi
⊢ IsDeduct Δ h1_psi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
apply IsDeduct.axiom_
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsDeduct Δ h1_phi
|
case a
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom h1_phi
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact h1_1
|
case a
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : IsAxiom h1_phi
⊢ IsAxiom h1_phi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact h2 h1_phi h1_1
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi : Formula
h1_1 : h1_phi ∈ Γ
⊢ IsDeduct Δ h1_phi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.T_14_16
|
[537, 1]
|
[550, 53]
|
exact IsDeduct.mp_ h1_phi h1_psi h1_ih_1 h1_ih_2
|
F : Formula
Δ Γ : Set Formula
h2 : ∀ H ∈ Γ, IsDeduct Δ H
h1_phi h1_psi : Formula
a✝¹ : IsDeduct Γ (h1_phi.imp_ h1_psi)
a✝ : IsDeduct Γ h1_phi
h1_ih_1 : IsDeduct Δ (h1_phi.imp_ h1_psi)
h1_ih_2 : IsDeduct Δ h1_phi
⊢ IsDeduct Δ h1_psi
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
simp only [IsProof] at h2
|
Q : Formula
Γ : Set Formula
h1 : IsDeduct Γ Q
h2 : ∀ P ∈ Γ, IsProof P
⊢ IsProof Q
|
Q : Formula
Γ : Set Formula
h1 : IsDeduct Γ Q
h2 : ∀ P ∈ Γ, IsDeduct ∅ P
⊢ IsProof Q
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
simp only [IsProof]
|
Q : Formula
Γ : Set Formula
h1 : IsDeduct Γ Q
h2 : ∀ P ∈ Γ, IsDeduct ∅ P
⊢ IsProof Q
|
Q : Formula
Γ : Set Formula
h1 : IsDeduct Γ Q
h2 : ∀ P ∈ Γ, IsDeduct ∅ P
⊢ IsDeduct ∅ Q
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.C_14_17
|
[553, 1]
|
[563, 28]
|
exact T_14_16 Q ∅ Γ h1 h2
|
Q : Formula
Γ : Set Formula
h1 : IsDeduct Γ Q
h2 : ∀ P ∈ Γ, IsDeduct ∅ P
⊢ IsDeduct ∅ Q
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_not
|
[566, 1]
|
[572, 32]
|
simp only [Formula.evalPrime]
|
P : Formula
V : VarBoolAssignment
⊢ evalPrime V P.not_ ↔ ¬evalPrime V P
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_imp
|
[575, 1]
|
[581, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
⊢ evalPrime V (P.imp_ Q) ↔ evalPrime V P → evalPrime V Q
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_false
|
[584, 1]
|
[589, 32]
|
simp only [Formula.evalPrime]
|
V : VarBoolAssignment
⊢ evalPrime V false_ ↔ False
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_and
|
[592, 1]
|
[598, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
⊢ evalPrime V (P.and_ Q) ↔ evalPrime V P ∧ evalPrime V Q
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_or
|
[601, 1]
|
[607, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
⊢ evalPrime V (P.or_ Q) ↔ evalPrime V P ∨ evalPrime V Q
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.eval_iff
|
[610, 1]
|
[616, 32]
|
simp only [Formula.evalPrime]
|
P Q : Formula
V : VarBoolAssignment
⊢ evalPrime V (P.iff_ Q) ↔ (evalPrime V P ↔ evalPrime V Q)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp only [Formula.IsTautoPrime]
|
⊢ true_.IsTautoPrime
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V true_
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp only [Formula.evalPrime]
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V true_
|
⊢ VarBoolAssignment → True
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_true
|
[619, 1]
|
[624, 7]
|
simp
|
⊢ VarBoolAssignment → True
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_1
|
[627, 1]
|
[632, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
⊢ (P.imp_ (Q.imp_ P)).IsTautoPrime
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V (P.imp_ (Q.imp_ P))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_1
|
[627, 1]
|
[632, 8]
|
tauto
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V (P.imp_ (Q.imp_ P))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_2
|
[635, 1]
|
[640, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q R : Formula
⊢ ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R))).IsTautoPrime
|
P Q R : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R)))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_2
|
[635, 1]
|
[640, 8]
|
tauto
|
P Q R : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.imp_ (Q.imp_ R)).imp_ ((P.imp_ Q).imp_ (P.imp_ R)))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
⊢ ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P)).IsTautoPrime
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
simp only [eval_not, eval_imp]
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.not_.imp_ Q.not_).imp_ (Q.imp_ P))
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), (¬evalPrime V P → ¬evalPrime V Q) → evalPrime V Q → evalPrime V P
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_prop_3
|
[643, 1]
|
[649, 8]
|
tauto
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), (¬evalPrime V P → ¬evalPrime V Q) → evalPrime V Q → evalPrime V P
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [Formula.IsTautoPrime] at h1
|
P Q : Formula
h1 : (P.imp_ Q).IsTautoPrime
h2 : P.IsTautoPrime
⊢ Q.IsTautoPrime
|
P Q : Formula
h1 : ∀ (V : VarBoolAssignment), evalPrime V (P.imp_ Q)
h2 : P.IsTautoPrime
⊢ Q.IsTautoPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [eval_imp] at h1
|
P Q : Formula
h1 : ∀ (V : VarBoolAssignment), evalPrime V (P.imp_ Q)
h2 : P.IsTautoPrime
⊢ Q.IsTautoPrime
|
P Q : Formula
h2 : P.IsTautoPrime
h1 : ∀ (V : VarBoolAssignment), evalPrime V P → evalPrime V Q
⊢ Q.IsTautoPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
simp only [Formula.IsTautoPrime] at h2
|
P Q : Formula
h2 : P.IsTautoPrime
h1 : ∀ (V : VarBoolAssignment), evalPrime V P → evalPrime V Q
⊢ Q.IsTautoPrime
|
P Q : Formula
h2 : ∀ (V : VarBoolAssignment), evalPrime V P
h1 : ∀ (V : VarBoolAssignment), evalPrime V P → evalPrime V Q
⊢ Q.IsTautoPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_mp
|
[652, 1]
|
[663, 8]
|
tauto
|
P Q : Formula
h2 : ∀ (V : VarBoolAssignment), evalPrime V P
h1 : ∀ (V : VarBoolAssignment), evalPrime V P → evalPrime V Q
⊢ Q.IsTautoPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
simp only [Formula.IsTautoPrime]
|
⊢ (false_.iff_ true_.not_).IsTautoPrime
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V (false_.iff_ true_.not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
simp only [eval_not, eval_iff]
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V (false_.iff_ true_.not_)
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V false_ ↔ ¬evalPrime V true_
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_false
|
[666, 1]
|
[671, 8]
|
tauto
|
⊢ ∀ (V : VarBoolAssignment), evalPrime V false_ ↔ ¬evalPrime V true_
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
⊢ ((P.and_ Q).iff_ (P.imp_ Q.not_).not_).IsTautoPrime
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.and_ Q).iff_ (P.imp_ Q.not_).not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
simp only [eval_and, eval_not, eval_imp, eval_iff]
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.and_ Q).iff_ (P.imp_ Q.not_).not_)
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V P ∧ evalPrime V Q ↔ ¬(evalPrime V P → ¬evalPrime V Q)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_and
|
[673, 1]
|
[679, 8]
|
tauto
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V P ∧ evalPrime V Q ↔ ¬(evalPrime V P → ¬evalPrime V Q)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
⊢ ((P.or_ Q).iff_ (P.not_.imp_ Q)).IsTautoPrime
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.or_ Q).iff_ (P.not_.imp_ Q))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
simp only [eval_or, eval_not, eval_imp, eval_iff]
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V ((P.or_ Q).iff_ (P.not_.imp_ Q))
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V P ∨ evalPrime V Q ↔ ¬evalPrime V P → evalPrime V Q
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_or
|
[681, 1]
|
[687, 8]
|
tauto
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment), evalPrime V P ∨ evalPrime V Q ↔ ¬evalPrime V P → evalPrime V Q
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
simp only [Formula.IsTautoPrime]
|
P Q : Formula
⊢ (((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_.IsTautoPrime
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment),
evalPrime V
(((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
simp only [eval_iff, eval_not, eval_imp]
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment),
evalPrime V
(((P.iff_ Q).imp_ ((P.imp_ Q).imp_ (Q.imp_ P).not_).not_).imp_
(((P.imp_ Q).imp_ (Q.imp_ P).not_).not_.imp_ (P.iff_ Q)).not_).not_
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment),
¬(((evalPrime V P ↔ evalPrime V Q) → ¬((evalPrime V P → evalPrime V Q) → ¬(evalPrime V Q → evalPrime V P))) →
¬(¬((evalPrime V P → evalPrime V Q) → ¬(evalPrime V Q → evalPrime V P)) → (evalPrime V P ↔ evalPrime V Q)))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.is_tauto_def_iff
|
[689, 1]
|
[695, 8]
|
tauto
|
P Q : Formula
⊢ ∀ (V : VarBoolAssignment),
¬(((evalPrime V P ↔ evalPrime V Q) → ¬((evalPrime V P → evalPrime V Q) → ¬(evalPrime V Q → evalPrime V P))) →
¬(¬((evalPrime V P → evalPrime V Q) → ¬(evalPrime V Q → evalPrime V P)) → (evalPrime V P ↔ evalPrime V Q)))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
induction F
|
F F' : Formula
h1 : F' ∈ F.primeSet
⊢ F'.IsPrime
|
case pred_const_
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ (pred_const_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
case pred_var_
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ (pred_var_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
case eq_
F' : Formula
a✝¹ a✝ : VarName
h1 : F' ∈ (eq_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
case true_
F' : Formula
h1 : F' ∈ true_.primeSet
⊢ F'.IsPrime
case false_
F' : Formula
h1 : F' ∈ false_.primeSet
⊢ F'.IsPrime
case not_
F' a✝ : Formula
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ a✝.not_.primeSet
⊢ F'.IsPrime
case imp_
F' a✝¹ a✝ : Formula
a_ih✝¹ : F' ∈ a✝¹.primeSet → F'.IsPrime
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (a✝¹.imp_ a✝).primeSet
⊢ F'.IsPrime
case and_
F' a✝¹ a✝ : Formula
a_ih✝¹ : F' ∈ a✝¹.primeSet → F'.IsPrime
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (a✝¹.and_ a✝).primeSet
⊢ F'.IsPrime
case or_
F' a✝¹ a✝ : Formula
a_ih✝¹ : F' ∈ a✝¹.primeSet → F'.IsPrime
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (a✝¹.or_ a✝).primeSet
⊢ F'.IsPrime
case iff_
F' a✝¹ a✝ : Formula
a_ih✝¹ : F' ∈ a✝¹.primeSet → F'.IsPrime
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (a✝¹.iff_ a✝).primeSet
⊢ F'.IsPrime
case forall_
F' : Formula
a✝¹ : VarName
a✝ : Formula
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (forall_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
case exists_
F' : Formula
a✝¹ : VarName
a✝ : Formula
a_ih✝ : F' ∈ a✝.primeSet → F'.IsPrime
h1 : F' ∈ (exists_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
case def_
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' ∈ (def_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case pred_const_ | pred_var_ =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ (pred_var_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case true_ | false_ =>
simp only [Formula.primeSet] at h1
simp at h1
|
F' : Formula
h1 : F' ∈ false_.primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case eq_ x y =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
x y : VarName
h1 : F' ∈ (eq_ x y).primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case not_ phi phi_ih =>
simp only [Formula.primeSet] at h1
exact phi_ih h1
|
F' phi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
h1 : F' ∈ phi.not_.primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case
imp_ phi psi phi_ih psi_ih
| and_ phi psi phi_ih psi_ih
| or_ phi psi phi_ih psi_ih
| iff_ phi psi phi_ih psi_ih =>
simp only [Formula.primeSet] at h1
simp at h1
tauto
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ (phi.iff_ psi).primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case forall_ x phi | exists_ x phi =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' ∈ (exists_ a✝ x).primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
case def_ =>
simp only [Formula.primeSet] at h1
simp at h1
subst h1
simp only [Formula.IsPrime]
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' ∈ (def_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ (pred_var_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ {pred_var_ a✝¹ a✝}
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' ∈ {pred_var_ a✝¹ a✝}
⊢ F'.IsPrime
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' = pred_var_ a✝¹ a✝
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
a✝¹ : PredName
a✝ : List VarName
h1 : F' = pred_var_ a✝¹ a✝
⊢ F'.IsPrime
|
a✝¹ : PredName
a✝ : List VarName
⊢ (pred_var_ a✝¹ a✝).IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
a✝¹ : PredName
a✝ : List VarName
⊢ (pred_var_ a✝¹ a✝).IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
h1 : F' ∈ false_.primeSet
⊢ F'.IsPrime
|
F' : Formula
h1 : F' ∈ ∅
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
h1 : F' ∈ ∅
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
x y : VarName
h1 : F' ∈ (eq_ x y).primeSet
⊢ F'.IsPrime
|
F' : Formula
x y : VarName
h1 : F' ∈ {eq_ x y}
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
x y : VarName
h1 : F' ∈ {eq_ x y}
⊢ F'.IsPrime
|
F' : Formula
x y : VarName
h1 : F' = eq_ x y
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
x y : VarName
h1 : F' = eq_ x y
⊢ F'.IsPrime
|
x y : VarName
⊢ (eq_ x y).IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
x y : VarName
⊢ (eq_ x y).IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' phi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
h1 : F' ∈ phi.not_.primeSet
⊢ F'.IsPrime
|
F' phi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
exact phi_ih h1
|
F' phi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ (phi.iff_ psi).primeSet
⊢ F'.IsPrime
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet ∪ psi.primeSet
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet ∪ psi.primeSet
⊢ F'.IsPrime
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet ∨ F' ∈ psi.primeSet
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
tauto
|
F' phi psi : Formula
phi_ih : F' ∈ phi.primeSet → F'.IsPrime
psi_ih : F' ∈ psi.primeSet → F'.IsPrime
h1 : F' ∈ phi.primeSet ∨ F' ∈ psi.primeSet
⊢ F'.IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' ∈ (exists_ a✝ x).primeSet
⊢ F'.IsPrime
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' ∈ {exists_ a✝ x}
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' ∈ {exists_ a✝ x}
⊢ F'.IsPrime
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' = exists_ a✝ x
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
a✝ : VarName
x : Formula
phi : F' ∈ x.primeSet → F'.IsPrime
h1 : F' = exists_ a✝ x
⊢ F'.IsPrime
|
a✝ : VarName
x : Formula
phi : exists_ a✝ x ∈ x.primeSet → (exists_ a✝ x).IsPrime
⊢ (exists_ a✝ x).IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
a✝ : VarName
x : Formula
phi : exists_ a✝ x ∈ x.primeSet → (exists_ a✝ x).IsPrime
⊢ (exists_ a✝ x).IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.primeSet] at h1
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' ∈ (def_ a✝¹ a✝).primeSet
⊢ F'.IsPrime
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' ∈ {def_ a✝¹ a✝}
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp at h1
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' ∈ {def_ a✝¹ a✝}
⊢ F'.IsPrime
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' = def_ a✝¹ a✝
⊢ F'.IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
subst h1
|
F' : Formula
a✝¹ : DefName
a✝ : List VarName
h1 : F' = def_ a✝¹ a✝
⊢ F'.IsPrime
|
a✝¹ : DefName
a✝ : List VarName
⊢ (def_ a✝¹ a✝).IsPrime
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.mem_primeSet_isPrime
|
[731, 1]
|
[770, 32]
|
simp only [Formula.IsPrime]
|
a✝¹ : DefName
a✝ : List VarName
⊢ (def_ a✝¹ a✝).IsPrime
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
subst h2
|
F F' : Formula
Δ_U : Set Formula
V : VarBoolAssignment
Δ_U' : Set Formula
h1 : ↑F.primeSet ⊆ Δ_U
h2 : Δ_U' = evalPrimeFfToNot V '' Δ_U
h3 : F' = evalPrimeFfToNot V F
⊢ IsDeduct Δ_U' F'
|
F F' : Formula
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑F.primeSet ⊆ Δ_U
h3 : F' = evalPrimeFfToNot V F
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) F'
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
subst h3
|
F F' : Formula
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑F.primeSet ⊆ Δ_U
h3 : F' = evalPrimeFfToNot V F
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) F'
|
F : Formula
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑F.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V F)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
induction F
|
F : Formula
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑F.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V F)
|
case pred_const_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : PredName
a✝ : List VarName
h1 : ↑(pred_const_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ a✝¹ a✝))
case pred_var_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : PredName
a✝ : List VarName
h1 : ↑(pred_var_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ a✝¹ a✝))
case eq_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ a✝ : VarName
h1 : ↑(eq_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ a✝¹ a✝))
case true_
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V true_)
case false_
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑false_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
case not_
Δ_U : Set Formula
V : VarBoolAssignment
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑a✝.not_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝.not_)
case imp_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ a✝ : Formula
a_ih✝¹ : ↑a✝¹.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝¹)
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(a✝¹.imp_ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (a✝¹.imp_ a✝))
case and_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ a✝ : Formula
a_ih✝¹ : ↑a✝¹.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝¹)
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(a✝¹.and_ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (a✝¹.and_ a✝))
case or_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ a✝ : Formula
a_ih✝¹ : ↑a✝¹.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝¹)
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(a✝¹.or_ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (a✝¹.or_ a✝))
case iff_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ a✝ : Formula
a_ih✝¹ : ↑a✝¹.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝¹)
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(a✝¹.iff_ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (a✝¹.iff_ a✝))
case forall_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : VarName
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(forall_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ a✝¹ a✝))
case exists_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : VarName
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(exists_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (exists_ a✝¹ a✝))
case def_
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : DefName
a✝ : List VarName
h1 : ↑(def_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ a✝¹ a✝))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case pred_const_ X xs =>
let F := pred_const_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_const_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case pred_var_ X xs =>
let F := pred_var_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_var_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case eq_ x y =>
let F := eq_ x y
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Δ_U : Set Formula
V : VarBoolAssignment
x y : VarName
h1 : ↑(eq_ x y).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (eq_ x y))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case true_ =>
apply IsDeduct.axiom_
apply IsAxiom.prop_true_
|
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑true_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V true_)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case false_ =>
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
simp
sorry
|
Δ_U : Set Formula
V : VarBoolAssignment
h1 : ↑false_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V false_)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case not_ phi phi_ih =>
simp only [Formula.primeSet] at h1
simp only [evalPrimeFfToNot] at phi_ih
simp only [evalPrimeFfToNot]
simp only [evalPrime]
simp
split_ifs
case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
apply IsDeduct.mp_ phi
apply proof_imp_deduct
apply T_14_6
exact phi_ih h1
case _ c1 =>
simp only [c1] at phi_ih
simp at phi_ih
exact phi_ih h1
|
Δ_U : Set Formula
V : VarBoolAssignment
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑phi.not_.primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi.not_)
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case forall_ x phi phi_ih =>
let F := forall_ x phi
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Δ_U : Set Formula
V : VarBoolAssignment
x : VarName
phi : Formula
phi_ih : ↑phi.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V phi)
h1 : ↑(forall_ x phi).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (forall_ x phi))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case def_ X xs =>
let F := def_ X xs
simp only [Formula.primeSet] at h1
simp at h1
simp only [evalPrimeFfToNot]
simp only [Formula.evalPrime]
apply IsDeduct.assume_
simp
apply Exists.intro F
tauto
|
Δ_U : Set Formula
V : VarBoolAssignment
X : DefName
xs : List VarName
h1 : ↑(def_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (def_ X xs))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
case and_ | or_ | iff_ | exists_ =>
sorry
|
Δ_U : Set Formula
V : VarBoolAssignment
a✝¹ : VarName
a✝ : Formula
a_ih✝ : ↑a✝.primeSet ⊆ Δ_U → IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V a✝)
h1 : ↑(exists_ a✝¹ a✝).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (exists_ a✝¹ a✝))
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
let F := pred_const_ X xs
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_const_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_const_ X xs).primeSet ⊆ Δ_U
F : Formula := pred_const_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.primeSet] at h1
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_const_ X xs).primeSet ⊆ Δ_U
F : Formula := pred_const_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑{pred_const_ X xs} ⊆ Δ_U
F : Formula := pred_const_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp at h1
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑{pred_const_ X xs} ⊆ Δ_U
F : Formula := pred_const_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [evalPrimeFfToNot]
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_const_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (pred_const_ X xs) then pred_const_ X xs else (pred_const_ X xs).not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.evalPrime]
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (pred_const_ X xs) then pred_const_ X xs else (pred_const_ X xs).not_)
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply IsDeduct.assume_
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_)
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ (if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_) ∈
(fun a => if evalPrime V a then a else a.not_) '' Δ_U
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ (if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_) ∈
(fun a => if evalPrime V a then a else a.not_) '' Δ_U
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U,
(if evalPrime V x then x else x.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply Exists.intro F
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ ∃ x ∈ Δ_U,
(if evalPrime V x then x else x.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
tauto
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_const_ X xs
h1 : pred_const_ X xs ∈ Δ_U
⊢ F ∈ Δ_U ∧
(if evalPrime V F then F else F.not_) =
if V (pred_const_ X xs) = true then pred_const_ X xs else (pred_const_ X xs).not_
|
no goals
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
let F := pred_var_ X xs
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_var_ X xs).primeSet ⊆ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_var_ X xs).primeSet ⊆ Δ_U
F : Formula := pred_var_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.primeSet] at h1
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑(pred_var_ X xs).primeSet ⊆ Δ_U
F : Formula := pred_var_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑{pred_var_ X xs} ⊆ Δ_U
F : Formula := pred_var_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp at h1
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
h1 : ↑{pred_var_ X xs} ⊆ Δ_U
F : Formula := pred_var_ X xs
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [evalPrimeFfToNot]
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct (evalPrimeFfToNot V '' Δ_U) (evalPrimeFfToNot V (pred_var_ X xs))
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (pred_var_ X xs) then pred_var_ X xs else (pred_var_ X xs).not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
simp only [Formula.evalPrime]
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if evalPrime V (pred_var_ X xs) then pred_var_ X xs else (pred_var_ X xs).not_)
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_)
|
https://github.com/pthomas505/FOL.git
|
097a4abea51b641d144539b9a0f7516f3b9d818c
|
FOL/NV/Margaris/Prop.lean
|
FOL.NV.L_15_7
|
[773, 1]
|
[916, 10]
|
apply IsDeduct.assume_
|
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ IsDeduct ((fun a => if evalPrime V a then a else a.not_) '' Δ_U)
(if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_)
|
case a
Δ_U : Set Formula
V : VarBoolAssignment
X : PredName
xs : List VarName
F : Formula := pred_var_ X xs
h1 : pred_var_ X xs ∈ Δ_U
⊢ (if V (pred_var_ X xs) = true then pred_var_ X xs else (pred_var_ X xs).not_) ∈
(fun a => if evalPrime V a then a else a.not_) '' Δ_U
|
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