The Lean 4 theorem `nsDiffH_shiftInvert_selects` in the `ChapterNavierStokesDiffHashimoto` chapter of the timepiece formalization

-- Generated from ChapterNavierStokesDiffHashimoto.lean — theorem BookProof.NavierStokesFlow.DiffHashimoto.nsDiffH_shiftInvert_selects
import Mathlib
import Definitions.Def_ChapterNavierStokesDiffHashimoto
import Definitions.Def_ChapterHashimotoComplexShifts
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.DiffHashimoto







open Filter Topology



open MvPolynomial
open BookProof.FarisLavine BookProof.HashimotoShiftInvert BookProof.EsaClosure
open BookProof.HermiteGalerkin
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.HermiteRelative
open BookProof.NavierStokesFlow.DifferentialL2

noncomputable section

variable (A : Matrix (Fin 3) (Fin 3) ℝ) (c : Fin 3 → ℝ)

set_option maxHeartbeats 4000000 in
-- The core operators unfold through several linear equivalences on a submodule of `L²(ℝ³)`,
-- so the default heartbeat budget is not enough.

theorem BookProof.NavierStokesFlow.DiffHashimoto.nsDiffH_shiftInvert_selects {γ : ℂ} (hγ : γ.im ≠ 0) :
    ∃ (Dom : Submodule ℂ (L2d 3)) (G : Dom →ₗ[ℂ] L2d 3) (X : L2d 3 →L[ℂ] L2d 3),
      IsSelfAdjointExtension ((polyGaussCore (d := 3)).subtype.comp (nsDiffH A c)) G ∧
      IsShiftInvertC G γ X ∧
      ‖X‖ ≤ |γ.im|⁻¹ ∧ Dom = LinearMap.range ((X : L2d 3 →ₗ[ℂ] L2d 3)) ∧
      (∀ (Dom' : Submodule ℂ (L2d 3)) (G' : Dom' →ₗ[ℂ] L2d 3), IsShiftInvertC G' γ X →
        Dom' = Dom ∧ ∀ (x : L2d 3) (hx : x ∈ Dom) (hx' : x ∈ Dom'),
          G' ⟨x, hx'⟩ = G ⟨x, hx⟩) := by sorry