reserve i, j, n for Element of NAT,
  f, g, h, k for FinSequence of REAL,
  M, N for non empty MetrSpace;

theorem Th2:
  for a, b, c, d, e, f being Real st a <= b+c & d <= e+f
   holds max(a,d) <= max(b,e) + max(c,f)
proof
  let a, b, c, d, e, f be Real;
  assume a <= b+c & d <= e+f;
  then
A1: max(a,d) <= max(b+c,e+f) by XXREAL_0:26;
  max(b+c,e+f) <= max(b,e) + max(c,f) by Th1;
  hence thesis by A1,XXREAL_0:2;
end;
