Section compression in binary order
= Section compression in binary order
{title2=$C_i$}
Fix a coordinate of the <Boolean hypercube>, delete it in each of the two sections, and replace each section by a <binary initial segment> of the same size. This preserves the total size. <Mathematical induction> on dimension proves that it does not decrease contained edge counts; the crossing contribution is the size of the section intersection, maximized by nested initial segments.