Definition regular_element_cha (H : complete_heyting_algebra) : complete_heyting_algebra. Proof. use make_complete_heyting_algebra. - exact (set_of_regular_elements H). - exact (regular_element_bounded_lattice H). - exact (regular_element_complete_lattice H). - exact (regular_element_exponential 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.