theorem Th4:
  V is non trivial implies for A st A is base holds A <> {}
proof
  assume
A1: V is non trivial;
  let A such that
A2: A is base and
A3: A = {};
A4: A = {}(the carrier of V) by A3;
  the ModuleStr of V = Lin A by A2,VECTSP_7:def 3
    .= (0).V by A4,MOD_3:6;
  hence contradiction by A1,LMOD_6:7;
end;
