The Lean 4 theorem `avgProj_apply` in the `ChapterGroupAverageEsa` chapter of the timepiece formalization

-- Generated from ChapterGroupAverageEsa.lean — theorem BookProof.GroupAverage.UnitaryRep.avgProj_apply
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterGraphCoreTransfer
import Definitions.Def_ChapterReducingSubspaceEsa
import Mathlib
import Definitions.Def_ChapterGroupAverageEsa
import Definitions.Def_ChapterMaschkeFiniteGroup
import Definitions.Def_ChapterWignerLittleGroup
open BookProof.ChapterMaschkeFiniteGroup
open BookProof.ChapterWignerLittleGroup
open BookProof.GroupAverage
open BookProof.GroupAverage



open BookProof.FarisLavine BookProof.GraphCore BookProof.ReducedEsa

noncomputable section

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {G : Type*} [Group G] [Fintype G]

variable (rep : UnitaryRep G F)
variable (G) in

theorem BookProof.GroupAverage.UnitaryRep.avgProj_apply (x : F) :
    rep.avgProj x = ((Fintype.card G : ℂ))⁻¹ • ∑ g : G, rep.act g x := by sorry