Definition RotInvIso_Mor (D : DTri) : TriMor D (InvRotDTri PT (RotDTri PT D)). Proof. use make_TriMor. - use make_MPMor. + use make_MPMorMors. * exact (AddEquivUnitIso Trans (Ob1 D)). * exact (identity _). * exact (identity _). + use make_MPMorComms. * exact (RotInvIso_Mor_Comm1 D). * exact (RotInvIso_Mor_Comm2 D). - exact (RotInvIso_Mor_Comm3 D). Defined.
Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.NaturalNumbers. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.NumberSystems.Integers. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Limits.Zero. Require Import UniMath.CategoryTheory.Limits.BinProducts. Require Import UniMath.CategoryTheory.Limits.BinCoproducts. Require Import UniMath.CategoryTheory.Limits.Equalizers. Require Import UniMath.CategoryTheory.Limits.Coequalizers. Require Import UniMath.CategoryTheory.Limits.Kernels. Require Import UniMath.CategoryTheory.Limits.Cokernels. Require Import UniMath.CategoryTheory.Limits.Pushouts. Require Import UniMath.CategoryTheory.Limits.Pullbacks. Require Import UniMath.CategoryTheory.Limits.BinDirectSums. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Abelian. Require Import UniMath.CategoryTheory.ShortExactSequences. Require Import UniMath.CategoryTheory.Categories.Abgr. Require Import UniMath.CategoryTheory.CategoriesWithBinOps. Require Import UniMath.CategoryTheory.PrecategoriesWithAbgrops. Require Import UniMath.CategoryTheory.PreAdditive. Require Import UniMath.CategoryTheory.Additive. Require Import UniMath.CategoryTheory.Morphisms. Require Import UniMath.CategoryTheory.AdditiveFunctors. Require Import UniMath.CategoryTheory.FiveLemma.