reserve n,m for Nat,
  r,r1,r2,s,t for Real,
  x,y for set;

theorem Th3:
  for r be Real holds 2*max+(r) = r + |.r.|
proof
  let r be Real;
  thus r + |.r.| = max+(r) - max-(r) + |.r.| by Th1
    .= max+(r) - max-(r) + (max+(r) + max-(r)) by Th2
    .= 2*max+(r);
end;
