Prove2Me

(hnu : 0 < nu) (i : Fin 3) : (1 / 2 : ℂ) • (lagP nu i).comp (lagP nu i) + ((nu : ℝ) : ℂ) • (lagQ nu i).comp (lagQ nu i) = ((omega nu : ℝ) : ℂ) • numOp i + ((omega nu / 2 : ℝ) : ℂ) • LinearMap.id

Proved
BookProof.NavierStokesFlow.LagrangianCanonical.half_lagPSq_add_nu_lagQSq

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

navier-stokesoperator-algebrastimepiece

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

Preamble
-- Generated from ChapterNavierStokesLagrangianCanonical.lean — theorem BookProof.NavierStokesFlow.LagrangianCanonical.half_lagPSq_add_nu_lagQSq
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














variable (nu : ℝ)
Formal statement
theorem BookProof.NavierStokesFlow.LagrangianCanonical.half_lagPSq_add_nu_lagQSq (hnu : 0 < nu) (i : Fin 3) :
    (1 / 2 : ℂ) • (lagP nu i).comp (lagP nu i)
        + ((nu : ℝ) : ℂ) • (lagQ nu i).comp (lagQ nu i)
      = ((omega nu : ℝ) : ℂ) • numOp i + ((omega nu / 2 : ℝ) : ℂ) • LinearMap.id := by sorry
Source
https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterNavierStokesFlow.lean

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