Prove2Me

`BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le` (p q : Fin m → ℝ) {v : Fin m → E} {C : ℝ} (hv : ∀ j, ‖v j‖ ≤ C) : ‖observableExpectation p v - observableExpect

Proved
BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionOutput.

BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le (p q : Fin m → ℝ) {v : Fin m → E} {C : ℝ} (hv : ∀ j, ‖v j‖ ≤ C) : ‖observableExpectation p v - observableExpectation q v‖ ≤ (∑ j, |p j - q j|) * C

Formalization note: Lean 4 identifier BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le.

Preamble
-- Generated from ChapterAttentionOutput.lean — theorem BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionOutput
import Definitions.Def_ChapterObservableExpectation
open BookProof.ChapterObservableExpectation
open BookProof.ChapterAttentionOutput


open scoped BigOperators

open Filter Topology

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m n : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionOutput.norm_observableExpectation_sub_le (p q : Fin m → ℝ) {v : Fin m → E} {C : ℝ}
    (hv : ∀ j, ‖v j‖ ≤ C) :
    ‖observableExpectation p v - observableExpectation q v‖ ≤ (∑ j, |p j - q j|) * C := by sorry

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