proposition: Lemma BinCoproductArrowUnique (a b : C) (CC : BinCoproductCocone a b) (x : C) (f : a --> x) (g : b --> x) (k : BinCoproductObject CC --> x) : BinCoproductIn1 CC · k = f → BinCoproductIn2 CC · k = g → k = BinCoproductArrow CC f g.
proof: Proof. intros H1 H2. use colimArrowUnique. simpl. intro u; induction u; simpl. - apply H1. - apply H2. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.EqDiag UniMath.CategoryTheory.Limits.BinCoproducts