 reserve x, y, y1, y2 for set;
 reserve V for Z_Module;
 reserve u, v, w for Vector of V;
 reserve F, G, H, I for FinSequence of V;
 reserve W, W1, W2, W3 for Submodule of V;
 reserve KL1, KL2 for Linear_Combination of V;
 reserve X for Subset of V;

theorem Th27:
  for p being prime Element of INT.Ring, V being free Z_Module holds
  ZMtoMQV(V,p,0. V) = 0.(Z_MQ_VectSp(V,p))
  proof
    let p be prime Element of INT.Ring, V be free Z_Module;
    thus 0.(Z_MQ_VectSp(V,p)) = 0.(VectQuot(V,p(*)V))
    .= zeroCoset(V,p(*)V) by VECTSP10:def 6
    .= ZMtoMQV(V,p,0. V) by ZMODUL01:59;
  end;
