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 mxcolK n B_ i : @submxcol n (\mxcol_i B_ i) i = B_ i.