proposition: Lemma isBinProduct'_to_isBinProduct : isBinProduct' -> isBinProduct _ _ _ p p1 p2.
proof: Proof. intros isBP' ? f g. apply (@iscontrweqf (hfiber (isBinProduct'_weq isBP' _) (make_dirprod f g))). - use weqfibtototal; intro; cbn. unfold postcomp_with_projections. apply pathsdirprodweq. - apply weqproperty. 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.Monics UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Products UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorCategory UniMath.Combinatorics.StandardFiniteSets