`BookProof.ChapterMackeyImprimitivity.cocycle_mem_stabilizer` (hs : ∀ x, s x • x₀ = x) (g : G) (x : X) : cocycle s g x ∈ MulAction.stabilizer G x₀

Proved

BookProof.ChapterMackeyImprimitivity.cocycle_mem_stabilizer

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterMackeyImprimitivity.

BookProof.ChapterMackeyImprimitivity.cocycle_mem_stabilizer (hs : ∀ x, s x • x₀ = x) (g : G) (x : X) : cocycle s g x ∈ MulAction.stabilizer G x₀

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

Preamble

-- Generated from ChapterMackeyImprimitivity.lean — theorem BookProof.ChapterMackeyImprimitivity.cocycle_mem_stabilizer
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.cocycle_mem_stabilizer (hs : ∀ x, s x • x₀ = x) (g : G) (x : X) :
    cocycle s g x ∈ MulAction.stabilizer G x₀ := by sorry

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