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

theorem Th1: :: !!! do XREAL
  for a, b, c, d being Real holds max(a+c,b+d) <= max(a,b) + max(c, d)
proof
  let a, b, c, d be Real;
  b <= max(a,b) & d <= max(c,d) by XXREAL_0:25;
  then
A1: b+d <= max(a,b) + max(c,d) by XREAL_1:7;
  a <= max(a,b) & c <= max(c,d) by XXREAL_0:25;
  then a+c <= max(a,b) + max(c,d) by XREAL_1:7;
  hence thesis by A1,XXREAL_0:28;
end;
