theorem oscillationEnergy_nonneg {H : Fin N → ℝ} (hH : ∀ n, 0 ≤ H n)
(ξ : Fin N → ℝ) :
0 ≤ oscillationEnergy H ξ := by
simp only [oscillationEnergy]
apply mul_nonneg
· norm_num
· exact Finset.sum_nonneg fun n _ => mul_nonneg (hH n) (sq_nonneg _)Core definitions for the Lean formalization of Paper 3: