theorem herfindahl_merger_formula {a_i a_j : ℝ} : (a_i + a_j) ^ 2 - a_i ^ 2 - a_j ^ 2 = 2 * a_i * a_j := by ring
thesis/CESProofs/Hierarchy/HerfindahlDynamics.lean:90
Herfindahl Dynamics: Entry, Exit, and Merger Effects on Concentration