= Essential disjointness of small subfamilies
{title2=$A_\eta^*=A_\eta\setminus\bigcup_{\nu<\eta}A_\nu$}
Any at-most-$\kappa$ subfamily of an <almost disjoint family on a regular cardinal> becomes pairwise disjoint after deleting fewer than $\kappa$ points from each member. Enumerate it in length at most $\kappa$ and apply the displayed trimming. Each removed part is a union of fewer than $\kappa$ small intersections, so <regular cardinal> arithmetic bounds it below $\kappa$.
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