subst ex
case himp.mp.intro.intro
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
h : ∀ {w' : M₁.Frame.World}, w ≺ w' → Satisfies M₁ w' p → Satisfies M₁ w' q
X : Unit ⊕ M₁.Frame.World ⊕ M₂.Frame.World
hWX : Sum.inr (Sum.inl w) ≺ X
hp : Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) X p
x : M₁.Frame.World
hx : w ≺ x
ex : Sum.inr (Sum.inl x) = X
⊢ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) X q
case himp.mp.intro.intro
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
h : ∀ {w' : M₁.Frame.World}, w ≺ w' → Satisfies M₁ w' p → Satisfies M₁ w' q
x : M₁.Frame.World
hx : w ≺ x
hWX : Sum.inr (Sum.inl w) ≺ Sum.inr (Sum.inl x)
hp : Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl x)) p
⊢ Satisfies (IntDPCounterexampleModel M₁ M₂ w₁ w₂) (Sum.inr (Sum.inl x)) q