Definition binaryProduct_pr_1_eqn {C:category} {a b:C} (prod : BinaryProduct a b) {c:C} (f : c --> a) (g : c --> b) : pr_1 prod ∘ binaryProductMap prod f g = f := maponpaths (HomPair_1 a b (opp_ob c)) (pr2 (pr1 (pr2 (pr2 prod) c (f,,g)))).
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import Require Import Require Import UniMath.MoreFoundations.Tactics.