Proposition cover_sharpen {P : coverage} {x y : X} (C : X → hProp) (p : y ≤ x) (q : P x C) : ∃ (C' : X → hProp), P y C' ∧ ∀ (z : X), C' z ⇒ ∃ (s : X), C s ∧ z ≤ s. Proof. exact (pr22 P x y C p q). Qed.
Require Import UniMath.Foundations.All. 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.Distributive. Require Import UniMath.OrderTheory.Lattice.Heyting. Require Import UniMath.OrderTheory.Lattice.CompleteHeyting. Require Import UniMath.OrderTheory.Lattice.Examples.FromPartialOrder.