theorem Th6: :: WAYBEL_2:6

for L being Semilattice
for D being non empty directed Subset of [:L,L:] holds union { X where X is non empty directed Subset of L : ex x being Element of L st
( X = {x} "/\" (proj2 D) & x in proj1 D ) } = (proj1 D) "/\" (proj2 D)