Section Vspace.
Variables (K : fieldType) (vT : vectType K).
Local Coercion dim : vectType >-> nat.
Definition b2mx n (X : n.-tuple vT) := \matrix_i v2r (tnth X i).
Let lin_b2mx n (X : n.-tuple vT) k :
\sum_(i < n) k i *: X`_i = r2v (\row_i k i *m b2mx X).
Fact memv_submod_closed U : submod_closed U.
Canonical memv_opprPred U := OpprPred (memv_submod_closed U).
Canonical memv_addrPred U := AddrPred (memv_submod_closed U).
Canonical memv_zmodPred U := ZmodPred (memv_submod_closed U).
Canonical memv_submodPred U := SubmodPred (memv_submod_closed U).

Lemma memv_suml I r (P : pred I) vs U :
(forall i, P i -> vs i \in U) -> \sum_(i <- r | P i) vs i \in U.