The Lean 4 theorem `lowOrder_relBound` in the `ChapterNavierStokesLagrangianKatoRellich` chapter of the timepiece formalization
ProvedBookProof.NavierStokesFlow.LagrangianKatoRellich.lowOrder_relBoundtimepiece
The Lean 4 theorem lowOrder_relBound in the ChapterNavierStokesLagrangianKatoRellich chapter of the timepiece formalization.
Preamble
-- Generated from ChapterNavierStokesLagrangianKatoRellich.lean — theorem BookProof.NavierStokesFlow.LagrangianKatoRellich.lowOrder_relBound
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.lowOrder_relBound {kap kap' cc : ℝ} (hkap : 0 ≤ kap) (hkap' : 0 ≤ kap') (hcc : 0 ≤ cc)
(hdrift : ∀ v : L.D,
‖(L.drift v : F)‖ ≤ kap * (∑ j : Fin 3, ‖(L.P j v : F)‖) + kap' * ‖(v : F)‖)
(hC : ∀ v : L.D, ‖(L.constraintOp v : F)‖ ≤ cc * ‖(v : F)‖) {a : ℝ} (ha : 0 < a) :
∃ b : ℝ, 0 ≤ b ∧ ∀ v : L.D,
‖(lowOrder L v : F)‖ ≤ a * ‖(secondOrder L v : F)‖ + b * ‖(v : F)‖ := by sorrySource