
theorem LmEMDetX6:
  for L being Z_Lattice, I being Subset of L
  holds I is Basis of L
  iff (MorphsZQ(L)).: I is Basis of EMbedding(L)
  proof
    let L be Z_Lattice, I be Subset of L;
    consider T be linear-transformation of L, EMbedding(L) such that
    A1: T is bijective and
    A2: T = MorphsZQ(L) and
    for v being Vector of L holds T.v = Class(EQRZM(L),[v,1])
    by ZMODUL08:21;
    thus thesis by A1,A2,ZMODUL06:49;
  end;
