proposition: Lemma to_In2_isMonic {a b : A} (B : BinDirectSum a b) : isMonic (to_In2 B).
proof: Proof. intros z f g H. apply (maponpaths (λ h : _, h · (to_Pr2 B))) in H. repeat rewrite <- assoc in H. set (X:= to_IdIn2 (A:=A) B). assert (X1 : to_In2 B · to_Pr2 B = 1%abgrcat). { apply X. } apply (@pathscomp0 _ _ ( f · (to_In2 B · to_Pr2 B)) _). - apply pathsinv0. etrans. { apply maponpaths. apply X1. } apply id_right. - etrans. { apply H. } etrans. { apply maponpaths. apply X1. } apply id_right. Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.MoreFoundations.Tactics UniMath.MoreFoundations.Notations UniMath.Algebra.BinaryOperations UniMath.Algebra.Groups UniMath.Algebra.Monoids UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis