Freiman repeated-three proof: equal contact

import Definitions.Def_Freiman_lowerJData
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Push
import Mathlib.Tactic.FinCases

open Freiman

theorem Freiman.lowerJ_equal_contact (hw : ∀ w : List ℕ+, lowerWidth w = (lowerBeta-lowerAlpha)/((((lowerCD w).1:ℝ)*lowerAlpha+(lowerCD w).2)*(((lowerCD w).1:ℝ)*lowerBeta+(lowerCD w).2))) (hc : (lowerTheta 66-lowerTheta 63)/(lowerTheta 90-lowerTheta 3) < (253/1000:ℝ) ∧ (7/5:ℝ)*(lowerTheta 68-lowerTheta 65)/(lowerTheta 28-lowerTheta 1) < (269/1000:ℝ) ∧ lowerTheta 3 < lowerTheta 30 ∧ lowerTheta 30 < lowerTheta 63 ∧ lowerTheta 63 < lowerTheta 66 ∧ lowerTheta 66 < lowerTheta 90 ∧ lowerTheta 65 < lowerTheta 68 ∧ lowerTheta 1 < lowerTheta 28 ∧ (19/5:ℝ)*(253/1000)*(26/25)<1 ∧ (269/1000:ℝ)<(253/1000)*(133/125)) (p : LowerPair) (ha : lowerAdmissible p) (hp : ¬ lowerMixed p) (hl : lowerEnds p.1 [3]) (hr : lowerEnds p.2 [3]) (hb : lowerParameterBox p) (hwide : lowerWidth p.2 ≤ lowerWidth p.1) (hratio : lowerWidth p.1 < (19/5:ℝ)*lowerWidth p.2) (hq : lowerJEqualQBounds p) : lowerJEqualContact p := by
  sorry