 reserve V for Z_Module;
 reserve W for Subspace of V;
 reserve v, u for Vector of V;
 reserve i for Element of INT.Ring;

theorem LmRank0a:
  for V being torsion-free Z_Module, v being Vector of V st v <> 0.V
  holds rank(Lin{v}) = 1
  proof
    let V be torsion-free Z_Module, v be Vector of V such that
    A1: v <> 0.V;
    v in Lin{v} by ZMODUL02:65,ZFMISC_1:31;
    then reconsider vv = v as Vector of Lin{v};
    A2: vv <> 0.Lin{v} by A1,ZMODUL01:26;
    (Omega).Lin{v} = Lin{vv} by ZMODUL03:20;
    hence thesis by A2,ZMODUL05:5;
  end;
