theorem curvatureK_eq_curvatureKH {J : ℕ} (hJ : 0 < J) {ρ : ℝ} :
curvatureK J ρ = curvatureKH ρ (1 / ↑J) := by
simp only [curvatureK, curvatureKH]
have hJr : (0 : ℝ) < ↑J := Nat.cast_pos.mpr hJ
have hJne : (J : ℝ) ≠ 0 := ne_of_gt hJr
field_simpCore definitions for the Lean formalization of Paper 1: