`BookProof.ChapterMackeyImprimitivity.mackeyMap_eq` (hs : ∀ x, s x • x₀ = x) (ψ : E) (x : X) : mackeyMap S s ψ x = S.p x₀ (S.U (s x)⁻¹ ψ)
ProvedBookProof.ChapterMackeyImprimitivity.mackeyMap_eqtheoremstimepiece
Prove the following Lean 4 theorem from ChapterMackeyImprimitivity.
BookProof.ChapterMackeyImprimitivity.mackeyMap_eq (hs : ∀ x, s x • x₀ = x) (ψ : E) (x : X) : mackeyMap S s ψ x = S.p x₀ (S.U (s x)⁻¹ ψ)
Formalization note: Lean 4 identifier BookProof.ChapterMackeyImprimitivity.mackeyMap_eq.
Preamble
-- Generated from ChapterMackeyImprimitivity.lean — theorem BookProof.ChapterMackeyImprimitivity.mackeyMap_eq
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_eq (hs : ∀ x, s x • x₀ = x) (ψ : E) (x : X) :
mackeyMap S s ψ x = S.p x₀ (S.U (s x)⁻¹ ψ) := by sorry