theorem Th24: :: DIOPHAN2:20

for a, b being Real
for n being Integer st (n - b) * ((n + 1) - a) > 0 & (a - n) * ((n + 1) - b) > 0 holds
( ((n - b) * ((n + 1) - a)) + ((a - n) * ((n + 1) - b)) = a - b & ((|.(a - n).| * |.(b - n).|) * |.((a - n) - 1).|) * |.((b - n) - 1).| <= (|.(a - b).| ^2) / 4 )