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

Proved

BookProof.NavierStokesFlow.SignFlip.saffH_conj_flip_inc

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

timepiece

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

Replaces the unuploadable node BookProof_NavierStokesFlow_SignFlip_saffH_conj_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.saffH_conj_flip_inc
import Mathlib
import Definitions.Def_ChapterNavierStokesSignFlip
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterStoneResolvent
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber.PairShift
open BookProof.NavierStokesFlow
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.saffH_conj_flip_inc {κ : ℝ} (hκ : 0 ≤ κ) {c : ℝ} (hc : c < 0)
    (x : maxDom (oscSymbol (affMu κ |c|))) :
    (flipU (fun n : ℕ => n) (affH hκ (abs_nonneg c) x) : L2I ℕ)
      = (saffH hκ c ⟨flipU (fun n : ℕ => n) (x : L2I ℕ),
          flipU_mem_maxDom _ (oscSymbol (affMu κ |c|)) x.2⟩ : L2I ℕ) := by sorry

Source

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

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