1≤i<j≤nT∈F,write T=(T\{})U{i} ifj∈T,itT,andT年F, otherwise. S(F)={S(T)|T∈F} 1.|Si(T)川=|T|and|Si(F)川=|Fl 2.F intersecting Sii(F)intersecting (2)the only bad case: A,B∈FA∩B={} A=A\{}U{}∈FB=B\{}U{i年Fi庄B > Ai∩B=0 contradiction!Sij (T) = ￾ Tij if j ￾ T,i ⇥￾ T, and Tij ⇥￾ F, T otherwise. 1 ￾ i<j ￾ n ⇥T ￾ F, write Tij = (T \ {j}) ⌅ {i} Sij (F) = {Sij (T) | T ￾ F} (2) the only bad case: A, B ￾ F A ￾ B = {j} i ⇥￾ B Aij ⇥ B = ￾ Aij = A \ {j} ⇤ {i} ￾ F Bij = B \ {j} ⌅ {i} ⇥￾ F contradiction! |Sij (T)| = |T| F intersecting Sij (F) intersecting 1. and 2. |Sij (F)| = |F|