The Lean 4 theorem `norm_P_sq_le` in the `ChapterNavierStokesLagrangianKatoRellich` chapter of the timepiece formalization

Proved

BookProof.NavierStokesFlow.LagrangianKatoRellich.norm_P_sq_le

by leonardopedro · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

timepiece

The Lean 4 theorem norm_P_sq_le in the ChapterNavierStokesLagrangianKatoRellich chapter of the timepiece formalization.

Preamble

-- Generated from ChapterNavierStokesLagrangianKatoRellich.lean — theorem BookProof.NavierStokesFlow.LagrangianKatoRellich.norm_P_sq_le
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianKatoRellich
import Definitions.Def_ChapterSirkBandLedger
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.LagrangianKatoRellich
open Filter Topology
open BookProof.NavierStokesFlow.FullEsa BookProof.NavierStokesFlow.LagrangianEsa BookProof.FarisLavine
open BookProof.EsaClosure BookProof.HashimotoShiftInvert BookProof.HermiteGalerkin
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable (L : LagrangianFullData F)

Formal statement

theorem BookProof.NavierStokesFlow.LagrangianKatoRellich.norm_P_sq_le (v : L.D) (i : Fin 3) :
    ‖(L.P i v : F)‖ ^ 2 ≤ 2 * (‖(v : F)‖ * ‖(secondOrder L v : F)‖) := by sorry

Source

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

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