(i : Fin 3) : (pos i).comp (pos i) + (mom i).comp (mom i) = (2 : ℂ) • numOp i + LinearMap.id

Proved

BookProof.NavierStokesFlow.LagrangianCanonical.posSq_add_momSq

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

navier-stokesoperator-algebrastimepiece

Lean 4 theorem BookProof.NavierStokesFlow.LagrangianCanonical.posSq_add_momSq (module BookProof.NavierStokesFlow), source chapter BookProof/ChapterNavierStokesFlow.lean.

Preamble

-- Generated from ChapterNavierStokesLagrangianCanonical.lean — theorem BookProof.NavierStokesFlow.LagrangianCanonical.posSq_add_momSq
import Mathlib
import Definitions.Def_ChapterNavierStokesLagrangianCanonical
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.LagrangianCanonical
















open scoped ENNReal



open BookProof.NavierStokesFlow.LpNat BookProof.FarisLavine BookProof.NavierStokesFlow.IkebeKato  BookProof.NavierStokesFlow.LagrangianKatoRellich
open BookProof.NavierStokesFlow.CanonicalVector BookProof.NavierStokesFlow.ThreeComponent

Formal statement

theorem BookProof.NavierStokesFlow.LagrangianCanonical.posSq_add_momSq (i : Fin 3) :
    (pos i).comp (pos i) + (mom i).comp (mom i)
      = (2 : ℂ) • numOp i + LinearMap.id := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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