Lemma 7.6
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This page proves a lemma for the m=13 case of FUNC.
Lemma 7.6:
If [math]\displaystyle{ \mathcal{A} }[/math] contains a size 5 set, then [math]\displaystyle{ \mathcal{A} }[/math] is Frankl's.
WLOG let that set be 12345. Let w(x)=6 is x=1, 2, 3, 4, 5 and w(x)=1 otherwise. The target weight is 35.
|K|=0:
In this case there are only two sets, the empty set and the full set 12345. The deficit is therefore 35+5=40.
|K|=1:
The only possible set in this case is the [math]\displaystyle{ C_5 }[/math] sets 12345 (as any smaller sets would violate the assumption).
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