proposition: Lemma limits_isBinCoproduct_from_isBinCoproductCocone (C : category) {a b c} (u : C ⟦ a, c⟧)(v : C ⟦ b, c⟧) : isBinCoproductCocone _ _ _ _ u v -> Limits.BinCoproducts.isBinCoproduct C a b c u v.
proof: Proof. intro h. set (CC := make_BinCoproductCocone _ _ _ _ _ _ h); simpl. intros x f g. use unique_exists; simpl. - apply (BinCoproducts.BinCoproductArrow CC f g). - abstract (split; [ apply (BinCoproducts.BinCoproductIn1Commutes _ _ _ CC) | apply (BinCoproducts.BinCoproductIn2Commutes _ _ _ CC)]). - abstract (intros h'; apply isapropdirprod; apply C). - intros h' [H1 H2]. eapply (BinCoproducts.BinCoproductArrowUnique _ _ _ CC). + exact H1. + exact H2. Defined.
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