Lemma ismonoidop_weq_fwd {X Y : UU} (H : X ≃ Y) (opp : binop X) : ismonoidop opp → ismonoidop (binop_weq_fwd H opp). Proof. intro is. split. apply isassoc_weq_fwd, (pr1 is). apply isunital_weq_fwd, (pr2 is). Defined.