`BookProof.NavierStokesFlow.HermiteFarisLavine.conj_hFun_mul` (κ : ℝ) (X Y : ℕ → ℂ) (m : ℕ) : (starRingEnd ℂ) (hFun κ X m) * Y m = -Complex.I * shift2 (crossA κ X Y) m + Complex.I

Proved

BookProof.NavierStokesFlow.HermiteFarisLavine.conj_hFun_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesHermiteFarisLavine.

BookProof.NavierStokesFlow.HermiteFarisLavine.conj_hFun_mul (κ : ℝ) (X Y : ℕ → ℂ) (m : ℕ) : (starRingEnd ℂ) (hFun κ X m) * Y m = -Complex.I * shift2 (crossA κ X Y) m + Complex.I * crossB κ X Y m

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

Preamble

-- Generated from ChapterNavierStokesHermiteFarisLavine.lean — theorem BookProof.NavierStokesFlow.HermiteFarisLavine.conj_hFun_mul
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.conj_hFun_mul (κ : ℝ) (X Y : ℕ → ℂ) (m : ℕ) :
    (starRingEnd ℂ) (hFun κ X m) * Y m
      = -Complex.I * shift2 (crossA κ X Y) m + Complex.I * crossB κ X Y m := by sorry

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