Variant mxsplits (V U : 'M_n) :=
  MxSplits (W : 'M_n) of mxmodule W & (U + W :=: V)%MS & mxdirect (U + W).

(* Specifications: *)
forall U, mxmodule U -> (U <= V)%MS -> mxsplits V U. Lemma mx_reducibleS U V :
Qed.
Qed.
Qed.