exact mult_by_scalars_comp.
Qed.
Hint Resolve mult_by_scalars_fun2_compatible mult_by_scalars_comp: algebra.

Lemma mult_by_scalars_Seqtl :
forall (R : ring) (V : module R) (N : Nat) (a : Map (fin N) R)
(v : Map (fin N) V),
mult_by_scalars (Seqtl a) (Seqtl v) =' Seqtl (mult_by_scalars a v) in _.