constructor
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
⊢ (∀ {p : Formula α}, □^[n]p ∈ Ω₁.theory → p ∈ Ω₂.theory) ↔ ∀ {p : Formula α}, p ∈ Ω₂.theory → ◇^[n]p ∈ Ω₁.theory
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
⊢ (∀ {p : Formula α}, □^[n]p ∈ Ω₁.theory → p ∈ Ω₂.theory) → ∀ {p : Formula α}, p ∈ Ω₂.theory → ◇^[n]p ∈ Ω₁.theory

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
⊢ (∀ {p : Formula α}, p ∈ Ω₂.theory → ◇^[n]p ∈ Ω₁.theory) → ∀ {p : Formula α}, □^[n]p ∈ Ω₁.theory → p ∈ Ω₂.theory