theorem ThTrivial2:
  for R being Ring
  for V being LeftMod of R, v being Vector of V st v <> 0.V holds
  Lin{v} is non trivial
  proof
    let R be Ring;
    let V be LeftMod of R, v be Vector of V such that
    A1: v <> 0.V;
    {v} <> {0.V} by A1,ZFMISC_1:3;
    then Lin{v} <> (0).V by MOD_3:7;
    then (Omega).Lin{v} <> (0).Lin{v} by VECTSP_4:36;
    hence thesis by ThTrivial1;
  end;
