proposition: Lemma isBinCoproduct_to_isBinCoproduct' : isBinCoproduct _ _ _ co i1 i2 -> isBinCoproduct'.
proof: Proof. intros isBCP ? fg. unfold hfiber, precomp_with_injections. apply (@iscontrweqf (∑ u : C ⟦ co, c ⟧, i1 · u = pr1 fg × i2 · u = pr2 fg)). - use weqfibtototal; intros to_prod. apply invweq, pathsdirprodweq. - exact (isBCP c (pr1 fg) (pr2 fg)). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.ProductCategory