| import Mathlib |
| import OAI.Probability.SKBarriers.Hierarchy.WeightedAugment |
| import OAI.Probability.SKBarriers.Locking.FourBlockTent |
|
|
| namespace OAI |
|
|
| section |
|
|
| noncomputable section |
| open scoped BigOperators |
| open Set |
| namespace SK.Analytic |
|
|
| theorem fourBlockTent_underlying (κ : ℝ) (b l j k : List (ℝ × ℝ)) : |
| weightedUnderlying (fourBlockTent κ b l j k)=(b++l)++(j++k) := by |
| simp [fourBlockTent] |
|
|
| theorem fourBlockTent_mass (κ : ℝ) (b l j k : List (ℝ × ℝ)) |
| (hm : ∀ p∈(b++l)++(j++k),p.1∈Icc (0:ℝ) 1) : |
| ∀ p∈fourBlockTent κ b l j k,p.1∈Icc (0:ℝ) 1 := by |
| apply (weighted_mass_iff _ (P:=fun x => x∈Icc (0:ℝ) 1)).mpr |
| rw [fourBlockTent_underlying] |
|
|
| theorem fourBlockTent_sorted (κ : ℝ) (b l j k : List (ℝ × ℝ)) |
| (hs : ((b++l)++(j++k)).Pairwise (fun p q => p.1≤q.1)) : |
| (fourBlockTent κ b l j k).Pairwise (fun p q => p.1≤q.1) := by |
| apply (weighted_sorted_iff _).mpr |
| rw [fourBlockTent_underlying] |
|
|
| def narrowTentError (μ B R ω : ℝ) : ℝ := 6*R^2+2*μ*B*ω+(B*ω)^2+B^2*ω |
| |
| theorem narrowTentError_mono {μ B R A ω : ℝ} (hμ : 0≤μ) (hB : 0≤B) (hA : 0≤A) (hAω : A≤ω) : |
| narrowTentError μ B R A≤narrowTentError μ B R ω := by |
| have HA := mul_le_mul_of_nonneg_left hAω hB |
| have HS := sq_le_sq₀ (mul_nonneg hB hA) (mul_nonneg hB (hA.trans hAω)) |
| have H1 := mul_le_mul_of_nonneg_left hAω (show 0≤2*μ*B by positivity) |
| have H2 := mul_le_mul_of_nonneg_left hAω (sq_nonneg B) |
| dsimp [narrowTentError] |
| nlinarith [(HS.mpr HA)] |
|
|
| end SK.Analytic |
|
|
| end |
| end |
|
|
| end OAI |
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|
