Lemma isrinv_weq_fwd {X Y : UU} (H : X ≃ Y) (opp : binop X) (x0 : X) (inv : X → X) : isrinv opp x0 inv → isrinv (binop_weq_fwd H opp) (H x0) (λ y : Y, H (inv (invmap H y))). Proof. intros is y. unfold binop_weq_fwd. apply maponpaths. refine (_ @ is _). apply (maponpaths (opp _)). apply homotinvweqweq. Defined.