Monic quadratic neg between

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Finset.Card
import Mathlib.Data.Int.GCD
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring

section
open scoped NumberField
open Module

namespace D1Bound5






theorem _root_.D1Bound5.monic_quadratic_neg_between (l u x b c : ℝ) (hlu : l < u)
    (hlx : l ≤ x) (hxu : x ≤ u)
    (hl : l^2+b*l+c < 0) (hu : u^2+b*u+c < 0) : x^2+b*x+c < 0 := by sorry







end D1Bound5
end