`BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg` (x : H) (a : ℝ) : G.genOp ⟨G.bAvg x a, G.bAvg_mem_genDomain x a⟩ = Complex.I • (G.U a x - x)

Proved

BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterStoneConverse.

BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg (x : H) (a : ℝ) : G.genOp ⟨G.bAvg x a, G.bAvg_mem_genDomain x a⟩ = Complex.I • (G.U a x - x)

Formalization note: Lean 4 identifier BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg.

Preamble

-- Generated from ChapterStoneConverse.lean — theorem BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg
import Mathlib
import Definitions.Def_ChapterStoneConverse
import Definitions.Def_ChapterStoneMeasurable
open BookProof.ChapterStoneMeasurable
open BookProof.ChapterStoneMeasurable


open scoped InnerProductSpace
open Filter Topology MeasureTheory


variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H]

variable [CompleteSpace H] [TopologicalSpace.SeparableSpace H]
variable (G : WeakMeasurableUnitaryGroup H)

Formal statement

theorem BookProof.ChapterStoneMeasurable.WeakMeasurableUnitaryGroup.genOp_bAvg (x : H) (a : ℝ) :
    G.genOp ⟨G.bAvg x a, G.bAvg_mem_genDomain x a⟩ = Complex.I • (G.U a x - x) := by sorry

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