
theorem Th30:
  for S1, S2 being non empty RelStr for D1 being Subset of S1, D2
  being Subset of S2 for x being Element of S1, y being Element of S2 st x
  is_>=_than D1 & y is_>=_than D2 holds [x,y] is_>=_than [:D1,D2:]
proof
  let S1, S2 be non empty RelStr, D1 be Subset of S1, D2 be Subset of S2, x be
  Element of S1, y be Element of S2 such that
A1: x is_>=_than D1 & y is_>=_than D2;
  let b be Element of [:S1,S2:];
  assume b in [:D1,D2:];
  then consider b1, b2 being object such that
A2: b1 in D1 and
A3: b2 in D2 and
A4: b = [b1,b2] by ZFMISC_1:def 2;
  reconsider b2 as Element of S2 by A3;
  reconsider b1 as Element of S1 by A2;
  b1 <= x & b2 <= y by A1,A2,A3;
  hence thesis by A4,Th11;
end;
