Definition rowval_gen m U :=
<<\matrix_ik
mxvec (\matrix_(i < m, k < d) (row i (val_gen U) *m A ^+ k)) 0 ik>>%MS.

Lemma rowval_genK m (U : 'M_(m,  nA)) : (in_gen (rowval_gen U) :=: U)%MS.