deletions | additions       diff --git a/Assume_we_are_comparing_two__.tex b/Assume_we_are_comparing_two__.tex  index de84251..899b725 100644  --- a/Assume_we_are_comparing_two__.tex  +++ b/Assume_we_are_comparing_two__.tex 
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\subsubsection{Heap Comparisons}  Assume we are comparing two intervals $A$ and $B$. Let $A$ be the interval stored in-heap and $B$ the interval we've just encountered. Our points of interest are the first end-point of $B$ which we denote $b_0$ and the point on $A$ which intersects the radial scan line at this point, which we refer to as $a_\alpha$. Our heap property is defined in terms of the distance of those points measured from $q$.  \begin{lem}