Lemma isBinCoproduct_to_isBinCoproduct' : isBinCoproduct _ _ _ co i1 i2 -> isBinCoproduct'. 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.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.Terminal. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Coproducts. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.ProductCategory.