reserve a,b,s,t,u,lambda for Real,
  n for Nat;
reserve x,x1,x2,x3,y1,y2 for Element of REAL n;

theorem :: EUCLID_2:24
  for x1,x2 being Element of REAL n holds |(-x1, -x2)| = |(x1, x2)|
proof
  let x1,x2 be Element of REAL n;
  thus |(-x1, -x2)| = - |(x1, -x2)| by Th23
    .= (-1)*|(x1, -x2)|
    .= (-1)*(- |(x1, x2)|) by Th23
    .= |(x1,x2)|;
end;
