Proposition regular_element_bounded_latticeop (H : complete_heyting_algebra) : bounded_latticeop (regular_element_lattice H) (bot_regular_element H) (top_regular_element H). Proof. split. - intro x ; use eq_regular_element ; cbn. rewrite cha_lunit_max_bot. rewrite is_regular_regular_element. apply idpath. - intro x ; use eq_regular_element ; cbn. rewrite cha_lunit_min_top. apply idpath. 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.