intro.
simpl in |- *.
red in |- *.
simpl in |- *.
intro.
generalize (span_ind_eqv_span S x).
intro.
unfold lin_comb_ind in H.
simpl in H.
unfold iff in H.
auto.
Qed.

(* Specifications: *)
Lemma span_ind_comp :
forall S S' : part_set V,
S =' S' in _ -> span_ind S =' span_ind S' in part_set V.