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135052a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | 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]; exact hm
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]; exact hs
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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