proposition: Lemma RoofEqclassToRoofComp {x y : ob C} (R : Roof x y) : RoofEqclassFromRoof R = RoofEqclassFromRoof (roof_comp (InvRoofFromMorInSom (RoofMor1 R) (RoofMor1Is R)) (MorToRoof (RoofMor2 R))).
proof: Proof. use RoofEqclassEqRoof. use (eqax1 (RoofEqclassIs (RoofEqclassFromRoof R))). - exact R. - exact (RoofDecomposeEqrel R). - apply RoofEqclassFromRoofIn. Defined.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors