Definition regular_element_lattice (H : complete_heyting_algebra) : lattice (set_of_regular_elements H). Proof. use make_lattice. - exact (λ x y, conj_regular_element x y). - exact (λ x y, disj_regular_element x y). - exact (regular_element_islatticeop 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.