∀ {α : Type u_1} (c : GeneralizedHeytingAlgebra α) (le : α → α → Prop) (eq_le : le = LE.le) (sup : α → α → α)
  (eq_sup : sup = max) (inf : α → α → α) (eq_inf : inf = min) (himp : α → α → α),
  himp = HImp.himp → ∀ (x x_1 x_2 : α), x ≤ himp x_1 x_2 ↔ x ⊓ x_1 ≤ x_2