Definition loopsBG_comp_2 (G:gr) (g h:G) : castTorsor (loopsBG G g) h = (h*g)%multmonoid. Proof. exact (torsor_univalence_inv_comp_eval (trivialTorsorAuto G g) h). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.Propositions. Require Import UniMath.MoreFoundations.Notations. Require Import UniMath.MoreFoundations.Univalence. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups. Require Import UniMath.OrderTheory.OrderedSets.OrderedSets. Import UniMath.MoreFoundations.PartA.