proposition: Lemma binaryProductMapUniqueness {C:category} {a b:C} (prod : BinaryProduct a b) {c:C} (f g : Hom C c (universalObject prod)) : pr_1 prod ∘ f = pr_1 prod ∘ g -> pr_2 prod ∘ f = pr_2 prod ∘ g -> f = g.
proof: Proof. intros r s. apply mapUniqueness. apply dirprodeq. exact r. exact s. Defined.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.RepresentableFunctors.Bifunctor UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics