proposition: Lemma RoofEqClassEq1 {x y : ob C} (R1 R2 : Roof x y) (H : (make_eqrel _ (RoofEqrel x y)) R1 R2) : (RoofEqclassFromRoof R1) = (RoofEqclassFromRoof R2).
proof: Proof. use RoofEqclassEq. - intros R HR. use (eqax1 (RoofEqclassIs (RoofEqclassFromRoof R2))). + exact R1. + use (eqax2 (RoofEqclassIs (RoofEqclassFromRoof R1))). * exact (RoofEqclassFromRoofIn R1). * exact HR. + use (eqax2 (RoofEqclassIs (RoofEqclassFromRoof R2))). * exact H. * exact (RoofEqclassFromRoofIn R2). - intros R HR. use (eqax1 (RoofEqclassIs (RoofEqclassFromRoof R1))). + exact R2. + use (eqax2 (RoofEqclassIs (RoofEqclassFromRoof R2))). * exact (RoofEqclassFromRoofIn R2). * exact HR. + use (eqax1 (RoofEqclassIs (RoofEqclassFromRoof R1))). * exact R1. * exact H. * exact (RoofEqclassFromRoofIn R1). Qed.
imports: UniMath.Foundations.PartD UniMath.Foundations.Propositions UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors