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 submxrow_matrix B_ j :
submxrow (\mxblock_(i, j) B_ i j) j = \mxcol_i B_ i j.