Lemma isBinCoproduct'_to_isBinCoproduct : isBinCoproduct' -> isBinCoproduct _ _ _ co i1 i2. Proof. intros isBCP' ? f g. apply (@iscontrweqf (hfiber (isBinCoproduct'_weq isBCP' _) (make_dirprod f g))). - use weqfibtototal; intro; cbn. unfold precomp_with_injections. apply pathsdirprodweq. - apply weqproperty. 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.