| import Mathlib |
| import OAI.Probability.SKBarriers.Locking.FourBlockTent |
| import OAI.Probability.SKBarriers.Locking.TentAtomMass |
|
|
| namespace OAI |
|
|
| section |
|
|
| noncomputable section |
| open scoped BigOperators |
| open Set |
| namespace SK.Analytic |
|
|
| theorem fourBlockTent_atom_le (κ : ℝ) (b l j k : List (ℝ × ℝ)) |
| (hl : 0<l.length) (hj : 0<j.length) {a d : ℝ} |
| (hlo : ∀ p∈l,a≤p.1) (hhi : ∀ p∈j,p.1≤d) : |
| scalarTentAtomMass (fourBlockTent κ b l j k).length (fun i => ((fourBlockTent κ b l j k).get i).1) |
| (fourBlockLeft κ b l j k) (fourBlockRight κ b l j k)≤d-a := by |
| have hls : fourBlockLeft κ b l j k<fourBlockRight κ b l j k := by |
| change b.length<b.length+l.length+j.length |
| omega |
| rw [scalarTentAtomMass_eq _ _ _ _ hls] |
| have HI := hhi (j.get ⟨j.length-1,by omega⟩) (List.get_mem ..) |
| have HL := hlo (l.get ⟨0,hl⟩) (List.get_mem ..) |
| have he1 : ((fourBlockTent κ b l j k).get |
| ⟨(fourBlockRight κ b l j k).val-1,by have := (fourBlockRight κ b l j k).isLt |
| (j.get ⟨j.length-1,by omega⟩).1 := by |
| simp only [List.get_eq_getElem,fourBlockTent,zeroWeightChain,constantWeightChain, |
| List.getElem_append,List.length_append,List.length_map] |
| simp (disch := omega) only [dite_eq_right,dite_eq_left,List.getElem_map] |
| congr 2 |
| omega |
| have he2 : ((fourBlockTent κ b l j k).get |
| ⟨(fourBlockLeft κ b l j k).val,by change b.length<(fourBlockTent κ b l j k).length |
| (l.get ⟨0,hl⟩).1 := by |
| simp only [List.get_eq_getElem,fourBlockTent,zeroWeightChain,constantWeightChain, |
| List.getElem_append,List.length_append,List.length_map] |
| simp (disch := omega) only [dite_eq_right,dite_eq_left,List.getElem_map,Nat.sub_self] |
| rw [he1,he2] |
| linarith |
|
|
| end SK.Analytic |
|
|
| end |
| end |
|
|
| end OAI |
|
|
