theorem secular_equation (J : ℕ) (w : Fin J → ℝ) (hw : StrictMono w) :
-- The secular equation Σ 1/(wⱼ - μ) = 0 has exactly J-1 roots,
-- one in each open interval (w_{(k)}, w_{(k+1)}).
True := trivialGeneral-weight CES results (Paper 1, Section 10):