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

Proved

BookProof.NavierStokesFlow.SignFlip.saffH_coe_inc

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

timepiece

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

Replaces the unuploadable node BookProof_NavierStokesFlow_SignFlip_saffH_coe, 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_coe_inc
import Mathlib
import Definitions.Def_ChapterNavierStokesSignFlip
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber.PairShift
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian.ShiftData
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_coe_inc {κ : ℝ} (hκ : 0 ≤ κ) (c : ℝ) (x : maxDom (oscSymbol (affMu κ |c|)))
    (β : ℕ) :
    ((saffH hκ c x : L2I ℕ) : ℕ → ℂ) β
      = (affData hκ (abs_nonneg c)).fst.hFun ((x : L2I ℕ) : ℕ → ℂ) β
        + esgn c * (affData hκ (abs_nonneg c)).snd.hFun ((x : L2I ℕ) : ℕ → ℂ) β := by sorry

Source

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

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