Proposition is_regular_conj {H : complete_heyting_algebra} (x y : regular_element H) : is_regular_element (x ∧ y). Proof. use make_is_regular_element. rewrite <- (is_regular_regular_element x). rewrite <- (is_regular_regular_element y). rewrite cha_conj_not. rewrite cha_not_not_not. apply cha_le_refl. 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. Require Import UniMath.OrderTheory.Lattice.DerivedLawsCompleteHeyting.