The Lean 4 theorem `invShiftOperator_selfAdjointCriterion` in the `ChapterHashimotoShiftInvert` chapter of the timepiece formalization

-- Generated from ChapterHashimotoShiftInvert.lean — theorem BookProof.HashimotoShiftInvert.invShiftOperator_selfAdjointCriterion
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterYangMillsFriedrichs
import Definitions.Def_ChapterYangMillsFriedrichsLimit
import Definitions.Def_ChapterHermiteGalerkinFriedrichs
import Mathlib
import Definitions.Def_ChapterHashimotoShiftInvert
import Definitions.Def_ChapterQgOuterFockFarisLavine
import Definitions.Def_ChapterComplexShiftCore
open BookProof.QgOuterFockFL
open BookProof.HashimotoShiftInvert

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



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

theorem BookProof.HashimotoShiftInvert.invShiftOperator_selfAdjointCriterion (R : F →L[ℂ] F) (hinj : Function.Injective R)
    (γ : ℝ) (hR : IsSelfAdjoint R) (w u : F)
    (hw : ∀ v : LinearMap.range (R : F →ₗ[ℂ] F),
      (inner ℂ (invShiftOperator R hinj γ v) w : ℂ) = inner ℂ (v : F) u) :
    ∃ h : w ∈ LinearMap.range (R : F →ₗ[ℂ] F), invShiftOperator R hinj γ ⟨w, h⟩ = u := by sorry