Definition isLeastUpperBound (E : hsubtype X) (lub : X) : UU := (isUpperBound E lub) × (isSmallerThanUpperBounds E lub).
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.BinaryOperations