intros.
red in |- *.
intros.
simpl in H0.
red in H0.
elim H0; intros.
elim H1; intros.
elim H2; intro.
simpl in |- *.
red in |- *.
exists x0.
exists x1.
exists (Map_include_map _ H x2).
apply Trans with (sum (mult_by_scalars x1 (Map_embed x2))); auto with algebra.
Qed.
Hint Resolve span_preserves_inclusion: algebra.

Lemma span_of_union :
forall S S' : part_set V,
span (union S S') =' span (union (span S) (span S')) in part_set V.