Prove2Me

`BookProof.NavierStokesFlow.AffineFiber.support_hFun` (S : ShiftData ι) (X : ι → ℂ) : Function.support (S.hFun X) ⊆ S.shift '' Function.support X ∪ S.shift ⁻¹' Function.support X

Proved
BookProof.NavierStokesFlow.AffineFiber.support_hFun

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.support_hFun (S : ShiftData ι) (X : ι → ℂ) : Function.support (S.hFun X) ⊆ S.shift '' Function.support X ∪ S.shift ⁻¹' Function.support X

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

Preamble
-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.support_hFun
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.support_hFun (S : ShiftData ι) (X : ι → ℂ) :
    Function.support (S.hFun X)
      ⊆ S.shift '' Function.support X ∪ S.shift ⁻¹' Function.support X := by sorry

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