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

Proved

BookProof.NavierStokesFlow.SignFlip.sblockFun_embFun_inc

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

timepiece

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

Replaces the unuploadable node BookProof_NavierStokesFlow_SignFlip_sblockFun_embFun, 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.sblockFun_embFun_inc
import Mathlib
import Definitions.Def_ChapterNavierStokesSignFlip
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesBilinearEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber.PairShift
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.SignFlip
open BookProof.NavierStokesFlow.BilinearEsa


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*}
variable {J : Type*}

Formal statement

theorem BookProof.NavierStokesFlow.SignFlip.sblockFun_embFun_inc (κ c : J → ℝ) (hκ : ∀ j, 0 ≤ κ j) (j : J) (a : ℕ → ℂ) :
    sblockFun κ c hκ (embFun j a)
      = embFun j (fun n => (affData (hκ j) (abs_nonneg (c j))).fst.hFun a n
          + esgn (c j) * (affData (hκ j) (abs_nonneg (c j))).snd.hFun a n) := by sorry

Source

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

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