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 mxcolP n (A B : 'M_(sp, n)) :
(forall i, submxcol A i = submxcol B i) <-> A = B.