proposition: Lemma isCoequalizerOutUnique {y z w: C} (f g : y --> z) (e : z --> w) (H : f · e = g · e) (E : isCoequalizer f g e H) (w0 : C) (h : z --> w0) (H' : f · h = g · h) (φ : w --> w0) (H'' : e · φ = h) : φ = (pr1 (pr1 (E w0 h H'))).
proof: Proof. set (T := tpair (fun ψ : w --> w0 => e · ψ = h) φ H''). set (T' := pr2 (E w0 h H') T). apply (base_paths _ _ T'). Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Retracts