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`BookProof.ChapterShannonSampling.half_add_period` : -(T / 2) + T = T / 2

Proved
BookProof.ChapterShannonSampling.half_add_period

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterShannonSampling.

BookProof.ChapterShannonSampling.half_add_period : -(T / 2) + T = T / 2

Formalization note: Lean 4 identifier BookProof.ChapterShannonSampling.half_add_period.

Preamble
-- Generated from ChapterShannonSampling.lean — theorem BookProof.ChapterShannonSampling.half_add_period
import Mathlib
import Definitions.Def_ChapterShannonSampling
open BookProof.ChapterShannonSampling



open MeasureTheory Complex AddCircle intervalIntegral Set
open scoped Real ComplexConjugate

variable {T : ℝ} [hT : Fact (0 < T)]

omit hT in
Formal statement
theorem BookProof.ChapterShannonSampling.half_add_period : -(T / 2) + T = T / 2 := by sorry

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