`BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct` (ψ : E) : ∑ x : X, S.U (s x) (mackeyMap S s ψ x) = ψ

Proved

BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMackeyImprimitivity.

BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct (ψ : E) : ∑ x : X, S.U (s x) (mackeyMap S s ψ x) = ψ

Formalization note: Lean 4 identifier BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct.

Preamble

-- Generated from ChapterMackeyImprimitivity.lean — theorem BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct
import Mathlib
import Definitions.Def_ChapterMackeyImprimitivity
open BookProof.ChapterMackeyImprimitivity


open scoped InnerProductSpace
open Finset


variable {G : Type*} [Group G] {X : Type*} [Fintype X] [MulAction G X]
variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E]

variable (S : ImprimitivitySystem G X E)
variable (S : ImprimitivitySystem G X E) (x₀ : X) (s : X → G)
variable {S x₀ s}

Formal statement

theorem BookProof.ChapterMackeyImprimitivity.mackeyMap_reconstruct (ψ : E) : ∑ x : X, S.U (s x) (mackeyMap S s ψ x) = ψ := by sorry

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