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 Th57:
  for n be non empty Nat,
     xv be Element of n -VectSp_over F_Real,
     xt be Element of TOP-REAL n
    st xv = xt
  holds -xv = -xt
  proof
    let n be non empty Nat,
       xv be Element of n -VectSp_over F_Real,
       xt be Element of TOP-REAL n;
    assume
    A1: xv=xt;

    thus -xv = (-1.F_Real)*xv by VECTSP_1:14
       .= (-1)*xt by A1,Th54
       .= -xt by RLVECT_1:16;
  end;
