fact: Definition exists_monotone {X:UU} (A B : X -> UU) : (forall x, A x -> B x) -> (∃ x, A x) -> ∃ x, B x.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.WellOrderedSets UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo