theorem Th33:
  -v*x = v*(-x) & w - v*x = w + v*(-x)
proof
A1: -v*x = (v*x) * (-1_R) by Th32
    .= v*(x* (-1_R)) by Def8
    .= v*(-(x* 1_R)) by VECTSP_1:8;
  hence -v* x = v*(-x);
  thus thesis by A1;
end;
