for I being non empty set
for J being non-Empty Poset-yielding ManySortedSet of I st ( for i being Element of I holds
( J . i is up-complete & J . i is lower-bounded ) ) holds
for x, y being Element of (product J) holds
( x << y iff ( ( for i being Element of I holds x . i << y . i ) & ex K being finite Subset of I st
for i being Element of I st not i in K holds
x . i = Bottom (J . i) ) )