(** - A vectorspace being a direct sum is only defined as a predicate; the sum_set
 however is defined as a construction:
%\tocdef{sum\_set}% *)
Definition sum_set (S1 S2 : part_set V) : part_set V.

Lemma subspace_sum_set : forall W1 W2 : part_set V, is_subspace W1 -> is_subspace W2 -> is_subspace (sum_set W1 W2).