intros.
red in |- *.
intros.
apply in_part_comp_r with (span_ind S:part_set V); auto with algebra.
simpl in |- *.
exists (Immediately (Build_subtype H)).
simpl in |- *.
apply Refl.
Qed.
End a_nice_fact_on_spans.
Hint Resolve set_included_in_its_span: algebra.
(** %\tocdef{generates}% *)
Definition generates (F : field) (V : vectorspace F)
(S W : part_set V) := span S =' W in part_set V.

(* Specifications: *)
Lemma generates_comp :
forall (F : field) (V : vectorspace F) (S S' W W' : part_set V),
S =' S' in _ -> W =' W' in _ -> generates S W -> generates S' W'.