The Lean 4 theorem `apply_eq` in the `ChapterHashimotoComplexShifts` chapter of the timepiece formalization

-- Generated from ChapterHashimotoComplexShifts.lean — theorem BookProof.HashimotoShiftInvert.IsShiftInvertC.apply_eq
import Mathlib
import Definitions.Def_ChapterHashimotoComplexShifts
open BookProof.HashimotoShiftInvert


















open BookProof.FarisLavine BookProof.YangMillsFriedrichs BookProof.YangMillsFriedrichsLimit
open BookProof.HermiteGalerkin
open Filter Topology




variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {Dom : Submodule ℂ F}

theorem BookProof.HashimotoShiftInvert.IsShiftInvertC.apply_eq {A : Dom →ₗ[ℂ] F} {γ : ℂ} {X : F →L[ℂ] F}
    (h : IsShiftInvertC A γ X) (u : F) :
    A ⟨X u, (h.2 u).choose⟩ = γ • X u - u := by sorry