`BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ` {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) (n : ℕ) : ((affH hκ hc (basisState κ c n) : L2I ℕ) : ℕ → ℂ) (n + 1) = Complex.I *...

Proved

BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) (n : ℕ) : ((affH hκ hc (basisState κ c n) : L2I ℕ) : ℕ → ℂ) (n + 1) = Complex.I * ((shear c n : ℝ) : ℂ)

Formalization note: Lean 4 identifier BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ.

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
import Definitions.Def_ChapterStoneResolvent
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow
open BookProof.NavierStokesFlow.AffineFiber


open scoped ENNReal



open LpNat BookProof.FarisLavine IkebeKato HermiteFarisLavine ShiftHamiltonian

variable {ι : Type*}

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
variable (P : PairShift ι)

Formal statement

theorem BookProof.NavierStokesFlow.AffineFiber.affH_coord_succ {κ c : ℝ} (hκ : 0 ≤ κ) (hc : 0 ≤ c) (n : ℕ) :
    ((affH hκ hc (basisState κ c n) : L2I ℕ) : ℕ → ℂ) (n + 1)
      = Complex.I * ((shear c n : ℝ) : ℂ) := by sorry

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