Producer for the exact step-down part (i) SectionFourIterate contract

theorem AVenhance.Infra.Section5.Contracts.sectionFourIterate_contract (β C₀ : ℝ) : ∃ (C : ℝ) (C₁ : ℝ), Integration.OnA8Instances β C₀ C₁ fun (I : Ingredients β) (_Φ : ℕ → ℝ → Homogenization.Vec 2 → ℝ) (_hΦ : IsStreamSeq I _Φ) (_κ : ℝ) (_M : ℕ) (_R : ℝ) (θ₀ : Homogenization.Vec 2 → ℝ) (m : ℕ) (_θm θprev : ℝ → Homogenization.Vec 2 → ℝ) (T : ℕ → ℝ → Homogenization.Vec 2 → ℝ) => Integration.SectionFourIterateContract I m θ₀ θprev T C

The step-down part (i) temperature closeness estimate in the contract shape. The V theorem is applied with a positive slack above twice the initial L2 norm, then the slack is eliminated by contradiction.