Canonical capmx_monoid n :=
Monoid.Law (@capmxA n n n n) (@cap1mx n) (@capmx1 n).
Canonical capmx_comoid n := Monoid.ComLaw (@capmxC n n n).

Lemma mxrank_injP m n p (A : 'M_(m, n)) (f : 'M_(n, p)) :
reflect (\rank (A *m f) = \rank A) ((A :&: kermx f)%MS == 0).