theorem Th32: :: BAGORDER:35

for R being non empty connected Poset
for x, y being Element of Fin the carrier of R holds
( [x,y] in union (rng (FinOrd-Approx R)) iff ( x = {} or ( x <> {} & y <> {} & PosetMax x <> PosetMax y & [(PosetMax x),(PosetMax y)] in the InternalRel of R ) or ( x <> {} & y <> {} & PosetMax x = PosetMax y & [(x \ {(PosetMax x)}),(y \ {(PosetMax y)})] in union (rng (FinOrd-Approx R)) ) ) )