theorem welfare_independent_of_own_sigma_weighted (c_n phi_n : ℝ) (σ₁ σ₂ : ℝ) (hσ₁ : σ₁ ≠ 0) (hσ₂ : σ₂ ≠ 0) : c_n * (phi_n / σ₁) * σ₁ = c_n * (phi_n / σ₂) * σ₂ := by field_simp
thesis/CESProofs/Hierarchy/SpectralHierarchy.lean:383
## Eigenstructure Bridge and Damping Cancellation with Weights