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 n be non empty Nat,
      xv, yv be Element of n -VectSp_over F_Real,
      xt, yt be Element of TOP-REAL n
    st xv = xt & yv = yt
  holds xv - yv = xt - yt
  proof
    let n be non empty Nat,
        xv, yv be Element of n -VectSp_over F_Real,
        xt, yt be Element of TOP-REAL n;
    assume
    A1: xv=xt & yv=yt; then
    -yv = -yt by Th57;
    hence xv - yv = xt - yt by A1,Th54;
  end;
