`BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero` (S : ShiftData ι) {X : ι → ℂ} {β : ι} (hpre : ∀ α, S.shift α = β → X α = 0) (hX : X (S.shift β) = 0) : S.hFun X β = 0

Proved

BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero (S : ShiftData ι) {X : ι → ℂ} {β : ι} (hpre : ∀ α, S.shift α = β → X α = 0) (hX : X (S.shift β) = 0) : S.hFun X β = 0

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero.

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesShiftHamiltonian
import Definitions.Def_ChapterStoneResolvent
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.ShiftHamiltonian
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian

variable {ι : Type*}

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

Formal statement

theorem BookProof.NavierStokesFlow.AffineFiber.hFun_eq_zero (S : ShiftData ι) {X : ι → ℂ} {β : ι}
    (hpre : ∀ α, S.shift α = β → X α = 0) (hX : X (S.shift β) = 0) : S.hFun X β = 0 := by sorry

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