reserve K for Ring,
  V1,W1 for VectSp of K;
reserve F for Field,
  V,W for VectSp of F;

theorem
  for V being finite-dimensional VectSp of F st card ([#]V) = 1 holds dim V = 0
proof
  let V be finite-dimensional VectSp of F such that
A1: card ([#]V) = 1;
  [#]V = {0.V}
  proof
    ex y being object st [#]V = {y} by A1,CARD_2:42;
    hence thesis by TARSKI:def 1;
  end;
  then (Omega).V = (0).V by VECTSP_4:def 3;
  hence thesis by VECTSP_9:29;
end;
