. intro h;
  obtain ⟨Γ, hΓ₁, hΓ₂⟩ := Context.provable_iff.mp h;
  apply Context.provable_iff.mpr;
  existsi Γ;
  constructor;
  . assumption;
  . exact FiniteContext.provable_iff.mpr $ imp_trans! (FiniteContext.provable_iff.mp hΓ₂) (conj₁'! multiboxDuality!);
case mp
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
Ω Ω₁ Ω₂ : MCT L
p : Formula α
n : ℕ
⊢ Ω.theory *⊢[L]! □^[n]p → Ω.theory *⊢[L]! ◇^[n](p ⟶ ⊥) ⟶ ⊥

case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
Ω Ω₁ Ω₂ : MCT L
p : Formula α
n : ℕ
⊢ Ω.theory *⊢[L]! ◇^[n](p ⟶ ⊥) ⟶ ⊥ → Ω.theory *⊢[L]! □^[n]p
case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
Ω Ω₁ Ω₂ : MCT L
p : Formula α
n : ℕ
⊢ Ω.theory *⊢[L]! ◇^[n](p ⟶ ⊥) ⟶ ⊥ → Ω.theory *⊢[L]! □^[n]p