File size: 1,832 Bytes
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 48 | 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; omega⟩).1=
(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; rw [fourBlockTent_length]; omega⟩).1=
(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
|