
theorem LmEMDetX4:
  for L, E being finite-rank free Z_Module
  st the ModuleStr of L = the ModuleStr of E
  holds rank L = rank E
  proof
    let L, E be finite-rank free Z_Module;
    assume AS: the ModuleStr of L = the ModuleStr of E;
    set I = the Basis of L;
    P1: rank L = card I by ZMODUL03:def 5;
    reconsider J = I as Subset of E by AS;
    J is Basis of E by LmEMDetX5,AS;
    hence thesis by P1,ZMODUL03:def 5;
  end;
