fact: Definition directed_set_coproduct_set_with_eq : ∃ (x : X), ∑ (D' : D → Y x) (HD : is_directed (Y x) D'), let DX := make_directed_set _ D D' HD in is_least_upperbound (coproduct_set_PartialOrder _ (λ x, Y x)) D (x ,, ⨆ DX) × (∏ (i : D), D i = (x ,, D' i)).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.OrderTheory.Posets UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous