
theorem LmEMDetX0:
  for L being Z_Lattice holds
  the ModuleStr of EMLat(L) = EMbedding(L)
  proof
    let L be Z_Lattice;
    Q1: the carrier of EMLat(L) = rng MorphsZQ(L) by defEMLat
    .= the carrier of EMbedding(L) by ZMODUL08:def 3;
    Q2: the ZeroF of EMLat(L) = zeroCoset(L) by defEMLat
    .= the ZeroF of EMbedding(L) by ZMODUL08:def 3;
    Q3: the addF of EMLat(L) = (addCoset(L)) || (rng MorphsZQ(L)) by defEMLat
    .= the addF of EMbedding(L) by ZMODUL08:def 3;
    Q4: the lmult of EMLat(L) = (lmultCoset(L)) | [:the carrier of INT.Ring,
    rng MorphsZQ(L):] by defEMLat
    .= the lmult of EMbedding(L) by ZMODUL08:def 3;
    thus the ModuleStr of EMLat(L) = EMbedding(L) by Q1,Q2,Q3,Q4;
  end;
