Proposition cha_and_monotone {H : complete_heyting_algebra} {x₁ x₂ y₁ y₂ : H} (p : x₁ ≤ x₂) (q : y₁ ≤ y₂) : (x₁ ∧ y₁) ≤ (x₂ ∧ y₂). Proof. use cha_min_le_case. - refine (cha_le_trans _ p). apply cha_min_le_l. - refine (cha_le_trans _ q). apply cha_min_le_r. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.OrderTheory.Lattice.Lattice. Require Import UniMath.OrderTheory.Lattice.Bounded. Require Import UniMath.OrderTheory.Lattice.Heyting. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting.