
theorem
  for L being Z_Lattice, b being FinSequence of L
  holds b is OrdBasis of L
  iff (MorphsZQ(L))*b is OrdBasis of EMLat(L)
  proof
    let L be Z_Lattice, b be FinSequence of L;
    P1: b is OrdBasis of L iff (MorphsZQ(L))*b is OrdBasis of EMbedding(L)
    by LmEMDetX8;
    the ModuleStr of EMLat(L) = the ModuleStr of EMbedding(L) by LmEMDetX0;
    hence thesis by P1,LmEMDetX9;
  end;
