fact: Definition Octa {PT : PreTriang} {x1 x2 y1 y2 z1 z2 : ob PT} {f1 : x1 --> y1} {f2 : y1 --> z2} {f3 : z2 --> (AddEquiv1 Trans x1)} {g1 : y1 --> z1} {g2 : z1 --> x2} {g3 : x2 --> (AddEquiv1 Trans y1)} {h2 : z1 --> y2} {h3 : y2 --> (AddEquiv1 Trans x1)} (H1 : isDTri (make_Tri f1 f2 f3)) (H2 : isDTri (make_Tri g1 g2 g3)) (H3 : isDTri (make_Tri (f1 · g1) h2 h3)) : UU := ∑ D : ((z2 --> y2) × (y2 --> x2)), (isDTri (make_Tri (dirprod_pr1 D) (dirprod_pr2 D) (g3 · (# (AddEquiv1 Trans) f2)))) × (dirprod_pr1 D · h3 = f3) × (h2 · dirprod_pr2 D = g2) × (f2 · dirprod_pr1 D = g1 · h2) × (dirprod_pr2 D · g3 = h3 · (# (AddEquiv1 Trans) f1)).
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