Definition regular_element_bounded_lattice (H : complete_heyting_algebra) : bounded_lattice (set_of_regular_elements H). Proof. use make_bounded_lattice. - exact (regular_element_lattice H). - exact (bot_regular_element H). - exact (top_regular_element H). - exact (regular_element_bounded_latticeop H). Defined.
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.