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).
Hint Resolve subvv : core.

Lemma subvPn {U V} : reflect (exists2 u, u \in U & u \notin V) (~~ (U <= V)%VS).