proposition: Proposition is_scott_continuous_equalizer_pr1 : is_scott_continuous equalizer_dcpo X pr1.
proof: Proof. use make_is_scott_continuous. - exact (Equalizer_pr1_monotone X Y f g). - intros D ; cbn. use antisymm_dcpo. + use dcpo_lub_is_least ; cbn. intro i. use less_than_dcpo_lub ; [ exact i | ] ; cbn. apply refl_dcpo. + use dcpo_lub_is_least ; cbn. intro i. use less_than_dcpo_lub ; [ exact i | ] ; cbn. apply refl_dcpo. Qed.
imports: UniMath.MoreFoundations.All UniMath.OrderTheory.Posets.Basics UniMath.OrderTheory.Posets.PointedPosets UniMath.OrderTheory.Posets.MonotoneFunctions UniMath.OrderTheory.DCPOs.Core.DirectedSets UniMath.OrderTheory.DCPOs.Core.Basics UniMath.OrderTheory.DCPOs.Core.ScottContinuous