A generalization of the AZ identity

Ahlswede R, Cai N. A generalization of the AZ identity. Combinatorica. 1993;13(3):241-247.The identity discovered in [1] can be viewed as a sharpening of the LYM inequality ([3], [4], [5]). It was extended in [2] so that it covers also Bollobás' inequality [6]. Here we present a further generalization and demonstrate that it shares with its predecessors the usefullness for uniqueness proofs in extremal set theory