intros.
simpl in |- *.
red in |- *.
simpl in |- *.
intro.
split.
intro.
apply is_lin_comb_comp with x S; auto with algebra.
intro.
apply is_lin_comb_comp with x S'; auto with algebra.
Qed.

(* Specifications: *)
(** - %\intoc{\bf Theorem 1.5}% *)
Lemma span_is_subspace : forall S : part_set V, is_subspace (span S).
intro; apply is_subspace_OK.