Lemma isinvongrquot {X : gr} (R : binopeqrel X) : isinv (@op (setwithbinopquot R)) (setquotpr R 1) (invongrquot R). Proof. split. - unfold islinv. apply (setquotunivprop R (λ x, _ = _)%logic). intro x. apply (@maponpaths _ _ (setquotpr R) ((x^-1) * x) 1). apply (grlinvax X). - unfold isrinv. apply (setquotunivprop R (λ x, _ = _)%logic). intro x. apply (@maponpaths _ _ (setquotpr R) (x / x) 1). apply (grrinvax X). Qed.
Require Import UniMath.MoreFoundations.Subtypes.