Definition subtype_binaryintersection_univ {X} (A B C : hsubtype X) : C ⊆ A ∩ B <-> C ⊆ A ∧ C ⊆ B. Proof. split. - intros C_AB. split; apply (istrans_subtype_containment C_AB). + apply subtype_binaryintersection_leq1. + apply subtype_binaryintersection_leq2. - cbn. intros [? ?]; split; auto. 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.