Definition exists_monotone {X:UU} (A B : X -> UU) : (forall x, A x -> B x) -> (∃ x, A x) -> ∃ x, B x. Proof. intros le_A_B. apply hinhfun, totalfun, le_A_B. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.