theorem Th9:
  for q be Element of TOP-REAL n,
      g be Element of REAL-NS n
    st q = g
  holds -q = -g
  proof
    let q be Element of TOP-REAL n,
        g be Element of REAL-NS n;
    assume
    A1: q = g;
    thus -q = (-1)*q by RLVECT_1:16
      .= (-1)*g by A1,Th8
      .= -g by RLVECT_1:16;
  end;
