| import Mathlib | |
| import OAI.Computability.MinUncut.Estimates.FaceUpdateSelf | |
| namespace OAI | |
| noncomputable section | |
| open scoped BigOperators | |
| open MeasureTheory ProbabilityTheory Filter | |
| open scoped Topology NNReal | |
| open scoped BigOperators | |
| open MeasureTheory ProbabilityTheory Polynomial Filter | |
| open scoped BigOperators Topology | |
| open MeasureTheory ProbabilityTheory WithLp | |
| open scoped BigOperators RealInnerProductSpace | |
| open scoped BigOperators | |
| namespace MinUncut.Slice | |
| open BinaryFourier | |
| open scoped BigOperators | |
| variable {W : Type*} [Fintype W] [AddCommGroup W] [Module F₂ W] | |
| local instance oddMaxTranslateDualFintype : Fintype (Module.Dual F₂ W) := BinaryFourier.dualFintype | |
| lemma oddMax_translate (one : W) (v : W → ℝ) (a : W) : | |
| oddMax one (fun b => v (a+b))=oddMax one v := by | |
| unfold oddMax | |
| congr 1 | |
| funext α | |
| rw [coefficient_translate, abs_mul, character_abs, one_mul] | |
| lemma processed_translate (H γ A : ℝ) (one : W) (v : W → ℝ) (a b : W) : | |
| processed H γ A one (fun t => v (a+t)) b=processed H γ A one v (a+b) := by | |
| unfold processed | |
| rw [expect_translate (fun t => (v t)^2) a, oddMax_translate] | |
| end MinUncut.Slice | |
| end | |
| end OAI | |