proposition: Lemma grfrompathsxy (X : gr) {a b : X} (e : a = b) : paths (op a (grinv X b)) (unel X).
proof: Proof. intros. set (e' := maponpaths (λ x : X, op x (grinv X b)) e). simpl in e'. rewrite (grrinvax X _) in e'. apply e'. Defined.
imports: UniMath.Algebra.Groups UniMath.Algebra.RigsAndRings