Section MaxRankSubMatrix.
Variables (m n : nat) (A : 'M_(m, n)).
Definition maxrankfun : 'I_m ^ \rank A :=
[arg max_(f > finfun (widen_ord (rank_leq_row A))) \rank (rowsub f A)].
Local Notation mxf := maxrankfun.

Lemma eq_maxrowsub : (rowsub mxf A :=: A)%MS.