theorem Th57: :: TOPS_5:57

for I being non empty set
for J being non-Empty TopStruct-yielding ManySortedSet of I
for P being non empty Subset of (product (Carrier J)) st P in product_prebasis J holds
ex i being Element of I st
( (proj (J,i)) .: P is open & ( for j being Element of I st j <> i holds
(proj (J,j)) .: P = [#] (J . j) ) )