Lemma isunit_weq_bck {X Y : UU} (H : X ≃ Y) (opp : binop Y) (x0 : Y) : isunit opp x0 → isunit (binop_weq_bck H opp) (invmap H x0). Proof. intro is. split. apply islunit_weq_bck, (pr1 is). apply isrunit_weq_bck, (pr2 is). Defined.