fact: Definition is_lower_bound_subfamily {I} (f : I -> P) {J} (g : J -> P) (ff : forall j, (image f) (g j)) {x} (x_lb : islowerbound f x) : islowerbound g x.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.WellOrderedSets UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo