The Lean 4 theorem `shiftH_flip` in the `ChapterNavierStokesSignFlip` chapter of the timepiece formalization

Proved

BookProof.NavierStokesFlow.SignFlip.shiftH_flip_inc

by leonardopedro · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

The Lean 4 theorem shiftH_flip in the ChapterNavierStokesSignFlip chapter of the timepiece formalization.

Replaces the unuploadable node BookProof_NavierStokesFlow_SignFlip_shiftH_flip, whose statement name is already declared inside its published definition bundle; the _inc suffix publishes the same statement as its own node.

Preamble

-- Generated from ChapterNavierStokesSignFlip.lean — theorem BookProof.NavierStokesFlow.SignFlip.shiftH_flip_inc
import Mathlib
import Definitions.Def_ChapterNavierStokesSignFlip
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
import Definitions.Def_ChapterStoneResolvent
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.SignFlip


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian AffineFiber

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

Formal statement

theorem BookProof.NavierStokesFlow.SignFlip.shiftH_flip_inc (S : ShiftData ι) (p : ι → ℕ) (k : ℕ)
    (hp : ∀ β, p (S.shift β) = p β + k) (x : maxDom S.sym) :
    (flipU p (ShiftData.shiftH S x) : L2I ι)
      = (-1 : ℂ) ^ k • (ShiftData.shiftH S ⟨flipU p (x : L2I ι),
          flipU_mem_maxDom p S.sym x.2⟩ : L2I ι) := by sorry

Source

https://github.com/leonardopedro/timepiece/blob/61595bc/BookProof/ChapterNavierStokesSignFlip.lean

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