Lemma BinProductPr1Commutes (a b : C) (P : BinProductCone a b): ∏ (c : C) (f : C⟦c,a⟧) (g : C⟦c,b⟧), BinProductArrow P f g · BinProductPr1 P = f. Proof. intros c f g. apply (limArrowCommutes P c (ProdCone f g) true). Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Limits.Graphs.Colimits. Require Import UniMath.CategoryTheory.Limits.Graphs.Limits.