for S1, S2 being non empty antisymmetric RelStr
for D1 being non empty Subset of S1
for D2 being non empty Subset of S2
for x being Element of S1
for y being Element of S2 st ( for c being Element of S1 st c is_>=_than D1 holds
x <= c ) & ( for d being Element of S2 st d is_>=_than D2 holds
y <= d ) holds
for b being Element of [:S1,S2:] st b is_>=_than [:D1,D2:] holds
[x,y] <= b