
theorem
  for L being Z_Lattice holds rank (L) = rank(EMLat(L))
  proof
    let L be Z_Lattice;
    consider T be linear-transformation of L, EMbedding(L) such that
    A1: T is bijective and
    T = MorphsZQ(L) and
    for v being Vector of L holds T.v = Class(EQRZM(L),[v,1])
    by ZMODUL08:21;
    P1: rank L = rank EMbedding(L) by A1,ZMODUL06:51;
    the ModuleStr of EMLat(L) = EMbedding(L) by LmEMDetX0;
    hence thesis by P1,LmEMDetX4;
  end;
