Fact memv_submod_closed U : submod_closed U.
Canonical memv_opprPred U := OpprPred (memv_submod_closed U).
Canonical memv_addrPred U := AddrPred (memv_submod_closed U).
Canonical memv_zmodPred U := ZmodPred (memv_submod_closed U).
Canonical memv_submodPred U := SubmodPred (memv_submod_closed U).

Lemma memvN U v : (- v \in U) = (v \in U). Proof. exact: rpredN. Qed.