Corners theorem
= Corners theorem
For every $\delta>0$, all sufficiently large integers $n$ have the property that every $A\subseteq[n]^2$ with $|A|\geq\delta n^2$ contains a <corner in an integer grid>. The <tripartite graph encoding of a grid> turns the absence of a corner into a family of many <edge-disjoint triangles> but only quadratically many total <triangles in a graph>, contradicting the <triangle removal lemma>.