theorem qPartitionFun_equal_payoffs (q T ε₀ : ℝ) : qPartitionFun J q T (fun _ => ε₀) = ↑(Fintype.card (Fin J)) * qExp q (ε₀ / T) := by simp [qPartitionFun, Finset.sum_const, nsmul_eq_mul]
thesis/CESProofs/Potential/Appendix.lean:90
Appendix Lemmas 1-3 (Paper 2, Appendix A)