constructor
case himp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) q
w : M₁.World
⊢ Satisfies M₁ w (p ⟶ q) ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) (p ⟶ q)
case himp.mp
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) q
w : M₁.World
⊢ Satisfies M₁ w (p ⟶ q) → Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) (p ⟶ q)

case himp.mpr
α : Type u_1
inst✝² : Inhabited α
inst✝¹ : DecidableEq α
inst✝ : Encodable α
p✝ q✝ : Formula α
M₁ M₂ : Model α
w₁ : M₁.World
w₂ : M₂.World
p q : Formula α
ihp : ∀ {w : M₁.World}, Satisfies M₁ w p ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) p
ihq : ∀ {w : M₁.World}, Satisfies M₁ w q ↔ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) q
w : M₁.World
⊢ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl w)) (p ⟶ q) → Satisfies M₁ w (p ⟶ q)