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

theorem Th20:
  for M, N being Reflexive non empty MetrStruct holds max-Prod2(
  M,N) is Reflexive
proof
  let M, N be Reflexive non empty MetrStruct;
  let a be Element of max-Prod2(M,N);
  consider x1, y1 being Point of M, x2, y2 being Point of N such that
A1: a = [x1,x2] & a = [y1,y2] and
A2: (the distance of max-Prod2(M,N)).(a,a) = max ((the distance of M).(
  x1,y1),(the distance of N).(x2,y2)) by Def1;
  the distance of M is Reflexive by METRIC_1:def 6;
  then
A3: (the distance of M).(x1,x1) = 0;
  the distance of N is Reflexive by METRIC_1:def 6;
  then
A4: (the distance of N).(x2,x2) = 0;
  x1 = y1 & x2 = y2 by A1,XTUPLE_0:1;
  hence thesis by A2,A3,A4;
end;
