Section semiring.
Variables (S : {pred R}) (ringS : semiringPred S) (kS : keyed_pred ringS).
Fact mxOver_mul_subproof : mulr_closed (@mxOver n.+1 n.+1 _ kS).

Lemma mxrowK m B_ j : @submxrow m (\mxrow_j B_ j) j = B_ j.