proposition: Lemma is_nat_trans_δ_genoption_mor (Ze : Ptd) : is_nat_trans (δ_source genopt Ze : functor C C) (δ_target genopt Ze : functor C C) (δ_genoption_mor Ze).
proof: Proof. intros a b f; simpl. induction Ze as [Z e]. unfold BinCoproduct_of_functors_mor; simpl. etrans. { apply precompWithBinCoproductArrow. } rewrite id_left. apply pathsinv0, BinCoproductArrowUnique. - etrans. { rewrite assoc. apply cancel_postcomposition, BinCoproductIn1Commutes. } rewrite <- assoc. etrans. { apply maponpaths, pathsinv0, (nat_trans_ax e). } simpl; rewrite assoc. apply cancel_postcomposition. etrans. { apply BinCoproductOfArrowsIn1. } now rewrite id_left. - rewrite assoc. etrans. { apply cancel_postcomposition, BinCoproductIn2Commutes. } rewrite <- !functor_comp. now apply maponpaths, BinCoproductOfArrowsIn2. Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.FunctorAlgebras UniMath.CategoryTheory.PointedFunctors UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.BicatOfCatsElementary UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.PointedFunctorsComposition