= Complementation of uniform intersecting families
{title2=$(r,t)\mapsto(n-r,n-2r+t)$}
Complementing all members preserves <cardinality> and gives $|A^c\cap B^c|=n-2r+|A\cap B|$. Thus complementation bijects <t-intersecting families> of $r$-sets with $(n-2r+t)$-intersecting families of $(n-r)$-sets. It swaps left and right <coordinate shifts of a set family>. When the transformed intersection parameter is positive, extremal families and their generating-support lemmas can therefore be compared in opposite compression directions.
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