Let trow_mul (m1 m2 n2 p2 : nat)
(A : 'rV_m1) (B1: 'M[F]_(m2,n2)) (B2 :'M[F]_(n2,p2)) :
trow A (B1 *m B2) = B1 *m trow A B2.

Lemma tprodE m1 n1 p1 (A1 :'M[F]_(m1,n1)) (A2 :'M[F]_(n1,p1))
m2 n2 p2 (B1 :'M[F]_(m2,n2)) (B2 :'M[F]_(n2,p2)) :
tprod (A1 *m A2) (B1 *m B2) = (tprod A1 B1) *m (tprod A2 B2).