Proposition lub_regular_element_pt_le {H : complete_heyting_algebra} {I : UU} (f f' : I → regular_element H) (p : ∏ (i : I), f i ≤ f' i) : lub_regular_element I f ≤ lub_regular_element I f'. Proof. use lub_regular_element_le. intro i. use le_lub_regular_element. - exact i. - apply p. 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.