proposition: Corollary idtoiso_FunctorAlg_commutes (X Y: FunctorAlg F)(e: X = Y): mor_from_algebra_mor F _ _ (morphism_from_z_iso _ _ (idtoiso e)) = idtoiso (maponpaths (alg_carrier F) e).
proof: Proof. unfold morphism_from_z_iso. rewrite eq_idtoiso_idtomor. etrans. 2: { apply pathsinv0, eq_idtoiso_idtomor. } apply idtomor_FunctorAlg_commutes. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.NNO