intros.
intro.
apply Trans with a; auto with algebra.
2: simpl in |- *.
2: apply Trans with a'; auto with algebra.
generalize
(concat_prop_per_part (A:=A) (n:=n) (m:=m) (v:=const_seq n a)
(w:=const_seq m a') (P:=eqa a)); intro.
simpl in H1.
destruct x.
apply H1; auto with algebra.
Qed.
End concat_const_seq.
Section mult_facts.
Variable F : field.
Variable V : vectorspace F.

(* Specifications: *)
Lemma mult_const_Zero :
forall (n : Nat) (v : seq n V),
mult_by_scalars (const_seq n (zero F)) v =' const_seq n (zero V) in seq _ _.