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
  for p,q be Element of TOP-REAL n,
      f,g be Element of REAL-NS n
    st p = f & q = g
  holds p-q = f-g
  proof
    let p,q be Element of TOP-REAL n,
        f,g be Element of REAL-NS n;
    assume
    A1: p=f & q=g; then
    -q = -g by Th9;
    hence p-q = f-g by A1,Th7;
  end;
