intros.
unfold mult_by_scalars in |- *.
auto with algebra.
Qed.
Hint Resolve mult_by_scalars_concat: algebra.

Lemma mult_by_scalars_modify_seq :
forall (F : field) (V : vectorspace F) (n : Nat) (p : seq n F)
(k : seq n V) (i : fin n) (q : F),
mult_by_scalars (modify_seq p i q) k ='
modify_seq (mult_by_scalars p k) i (q mX k i) in seq _ _.