Section mxOverMul.
Variables (S : predPredType R) (ringS : semiringPred S) (kS : keyed_pred ringS).

Lemma mxOverM p q r : {in mxOver kS & mxOver kS,
forall u : 'M[R]_(p, q), forall v : 'M[R]_(q, r), u *m v \is a mxOver kS}.