The Lean 4 theorem `cocycle_mem_stabilizer` in the `ChapterMackeyGeneralBase` chapter of the timepiece formalization

-- Generated from ChapterMackeyGeneralBase.lean — theorem BookProof.ChapterMackeyGeneralBase.cocycle_mem_stabilizer
import Mathlib
import Definitions.Def_ChapterMackeyGeneralBase
import Definitions.Def_ChapterMackeyImprimitivity
import Definitions.Def_ChapterA4
open BookProof.ChapterMackeyImprimitivity
open BookProof.ChapterMackeyImprimitivity
open BookProof.ChapterMackeyGeneralBase

variable {G : Type*} [Group G] {X : Type*} [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}


open scoped InnerProductSpace

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