proposition: Lemma DTriCompZero (D : @DTri PT) : Mor1 D · Mor2 D = ZeroArrow (to_Zero PT) _ _.
proof: Proof. set (D2 := TrivialDTri PT (Ob1 D)). set (Ext' := DExt PT D2 D (identity (Ob1 D)) (Mor1 D) (idpath _)). use (squash_to_prop Ext'). - apply to_has_homsets. - intros Ext. clear Ext'. set (M := TExtMor Ext). use (pathscomp0 (MPComm2 M)). cbn. apply ZeroArrow_comp_left. Qed.
imports: UniMath.Tactics.EnsureStructuredProofs UniMath.Foundations.UnivalenceAxiom UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.Foundations.NaturalNumbers UniMath.Algebra.BinaryOperations UniMath.Algebra.Monoids UniMath.NumberSystems.Integers UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Limits.Zero UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.BinCoproducts UniMath.CategoryTheory.Limits.Equalizers UniMath.CategoryTheory.Limits.Coequalizers UniMath.CategoryTheory.Limits.Kernels UniMath.CategoryTheory.Limits.Cokernels UniMath.CategoryTheory.Limits.Pushouts UniMath.CategoryTheory.Limits.Pullbacks UniMath.CategoryTheory.Limits.BinDirectSums UniMath.CategoryTheory.Monics UniMath.CategoryTheory.Epis UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Abelian UniMath.CategoryTheory.ShortExactSequences UniMath.CategoryTheory.Categories.Abgr UniMath.CategoryTheory.CategoriesWithBinOps UniMath.CategoryTheory.PrecategoriesWithAbgrops UniMath.CategoryTheory.PreAdditive UniMath.CategoryTheory.Additive UniMath.CategoryTheory.Morphisms UniMath.CategoryTheory.AdditiveFunctors UniMath.CategoryTheory.FiveLemma