proposition: Lemma EqualizerInEq {a b : C} {f g : C⟦a, b⟧} (E : Equalizer f g) (e : C) (h h' : C⟦e, EqualizerObject E⟧) (H : h · EqualizerArrow E = h' · EqualizerArrow E) : h = h'.
proof: Proof. refine (EqualizerInUnique E e (h' · EqualizerArrow E) _ h H @ !EqualizerInUnique E e (h' · EqualizerArrow E) _ h' (idpath _)). do 2 refine (assoc' _ _ _ @ !_). apply maponpaths. apply EqualizerArrowEq. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Graphs.Limits UniMath.CategoryTheory.Limits.Graphs.Colimits UniMath.CategoryTheory.Limits.Equalizers