proposition: Lemma isEqualizer'_to_isEqualizer : isEqualizer' -> isEqualizer f g h H.
proof: Proof. intros isEq' E' h' H'. apply (@iscontrweqf (hfiber (isEqualizer'_weq isEq' _) (h',, H'))). - cbn; unfold hfiber. use weqfibtototal; intros j; cbn. unfold postcomp_with_equalizer_mor. apply subtypeInjectivity. intro; apply C. - apply weqproperty. Defined.
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