proposition: Lemma EqualizerInComp {y z : C} {f g : y --> z} (E : Equalizer f g) {x x' : C} (h1 : x --> x') (h2 : x' --> y) (H1 : h1 · h2 · f = h1 · h2 · g) (H2 : h2 · f = h2 · g) : EqualizerIn E x (h1 · h2) H1 = h1 · EqualizerIn E x' h2 H2.
proof: Proof. use EqualizerInsEq. rewrite EqualizerCommutes. rewrite <- assoc. rewrite EqualizerCommutes. apply idpath. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Retracts