reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

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;
