
theorem ThRankrEM1:
  for V being finite-rank free Z_Module, r being non zero Element of F_Rat
  holds rank(EMbedding(r, V)) = rank(EMbedding(V))
  proof
    let V be finite-rank free Z_Module, r be non zero Element of F_Rat;
    consider T be linear-transformation of EMbedding(V),EMbedding(r,V)
    such that
    A1: (for v being Element of Z_MQ_VectSp(V) st v in EMbedding(V)
    holds T.v = r*v) &
    T is bijective by rSB03A;
    thus thesis by A1,ZMODUL06:51;
  end;
