Definition regular_element_complete_lattice (H : complete_heyting_algebra) : is_complete_lattice (regular_element_bounded_lattice H). Proof. use complete_lattice_from_glb. intros I f. refine (glb_regular_element f ,, _). apply is_glb_glb_regular_element. 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.