reserve x,y for Element of REAL;
reserve i,j,k for Element of NAT;
reserve a,b for Element of REAL;

theorem
  for x,y being Element of REAL holds *(opp x,y) = opp *(x,y)
proof
  let x,y be Element of REAL;
  +(*(opp x,y),*(x,y)) = *(+(opp x,x), y) by Th14
    .= 0 by Th12,Def3;
  hence thesis by Def3;
end;
