theorem eigenvalue_perp_pos_substitute (hJ : 0 < J) {ρ : ℝ} (hρ : 1 < ρ)
{c : ℝ} (hc : 0 < c) :
0 < cesEigenvaluePerp J ρ c := by
simp only [cesEigenvaluePerp]
exact div_pos (neg_pos.mpr (by linarith)) (mul_pos (Nat.cast_pos.mpr hJ) hc)Substitute Regime: The ρ > 1 Theory (Anti-Complementarity)