End BigSum.
(* Intersection *)

(* Specifications: *)
Lemma subv_cap U V W : (U <= V :&: W)%VS = (U <= V)%VS && (U <= W)%VS.
Lemma vspace_modr  U V W : (W <= U -> (U :&: V) + W = U :&: (V + W))%VS.
End BigCap.
(* Complement *)
Lemma addv_complf U : (U + U^C)%VS = fullv.
Lemma capv_compl U : (U :&: U^C = 0)%VS.
(* Difference *)
Lemma diffvSl U V : (U :\: V <= U)%VS.
Lemma addv_diff_cap U V : (U :\: V + U :&: V)%VS = U.
Lemma addv_diff U V : (U :\: V + V = U + V)%VS.
Lemma diffv_eq0 U V : (U :\: V == 0)%VS = (U <= V)%VS.
Lemma dimv_leq_sum I r (P : pred I) (Us : I -> {vspace vT}) :
\dim (\sum_(i <- r | P i) Us i) <= \sum_(i <- r | P i) \dim (Us i).