reserve D for non empty set,
  D1,D2,x,y for set,
  n,k for Nat,
  p,x1 ,r for Real,
  f for Function;
reserve F for Functional_Sequence of D1,D2;
reserve G,H,H1,H2,J for Functional_Sequence of D,REAL;

theorem
  -H = (-1)(#)H
proof
  now
    let n be Element of NAT;
    thus (-H).n = -H.n by Def3
      .=((-1)(#)H).n by Def1;
  end;
  hence thesis by FUNCT_2:63;
end;
