`BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le` (hκ : 0 ≤ κ) (X : ℕ → ℂ) (m : ℕ) : ‖hFun κ X m‖ ^ 2 ≤ 2 * shift2 (fun n => (ampSeq κ X n) ^ 2) m + 2 * (ampSeq...

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le (hκ : 0 ≤ κ) (X : ℕ → ℂ) (m : ℕ) : ‖hFun κ X m‖ ^ 2 ≤ 2 * shift2 (fun n => (ampSeq κ X n) ^ 2) m + 2 * (ampSeq κ X (m + 2)) ^ 2

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le.

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le
import Mathlib
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.HermiteFarisLavine


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato

variable {κ : ℝ}
variable {x : maxDom (oscSymbol κ)}

Formal statement

theorem BookProof.NavierStokesFlow.HermiteFarisLavine.normSq_hFun_le (hκ : 0 ≤ κ) (X : ℕ → ℂ) (m : ℕ) :
    ‖hFun κ X m‖ ^ 2
      ≤ 2 * shift2 (fun n => (ampSeq κ X n) ^ 2) m + 2 * (ampSeq κ X (m + 2)) ^ 2 := by sorry

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