Proposition cha_not_antimonotone {H : complete_heyting_algebra} {x y : H} (p : y ≤ x) : ¬ x ≤ ¬ y. Proof. use cha_to_le_exp. refine (cha_le_trans _ _). { exact (cha_and_monotone_r p). } use cha_exp_eval. 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.