
theorem
  for V being torsion-free Z_Module, vv being Vector of EMbedding(V)
  holds ex v being Vector of V st (MorphsZQ(V)).v = vv
  proof
    let V be torsion-free Z_Module, vv be Vector of EMbedding(V);
    set Z = EMbedding(V);
    consider T be linear-transformation of V, Z such that
    A1: T is bijective & T = MorphsZQ(V) &
    (for v being Element of V holds T.v = Class(EQRZM(V),[v,1])) by SB03;
    vv in the carrier of Z;
    then vv in rng MorphsZQ(V) by A1,FUNCT_2:def 3;
    then consider v be object such that
    A2: v in the carrier of V & vv = (MorphsZQ(V)).v by FUNCT_2:11;
    reconsider v as Vector of V by A2;
    take v;
    thus thesis by A2;
  end;
