
theorem
  for L being Z_Lattice, I being Subset of L
  holds I is Basis of L
  iff (MorphsZQ(L)).: I is Basis of EMLat(L)
  proof
    let L be Z_Lattice, I be Subset of L;
    P1: I is Basis of L iff (MorphsZQ(L)).: I is Basis of EMbedding(L)
    by LmEMDetX6;
    the ModuleStr of EMLat(L) = the ModuleStr of EMbedding(L) by LmEMDetX0;
    hence thesis by P1,LmEMDetX5;
  end;
