`BookProof.NavierStokesFlow.AffineFiber.basisState_coe` (κ c : ℝ) (n m : ℕ) : ((basisState κ c n : L2I ℕ) : ℕ → ℂ) m = if m = n then 1 else 0

Proved

BookProof.NavierStokesFlow.AffineFiber.basisState_coe

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNavierStokesAffineFiberEsa.

BookProof.NavierStokesFlow.AffineFiber.basisState_coe (κ c : ℝ) (n m : ℕ) : ((basisState κ c n : L2I ℕ) : ℕ → ℂ) m = if m = n then 1 else 0

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

Preamble

-- Generated from ChapterNavierStokesAffineFiberEsa.lean — theorem BookProof.NavierStokesFlow.AffineFiber.basisState_coe
import Mathlib
import Definitions.Def_ChapterNavierStokesAffineFiberEsa
import Definitions.Def_ChapterNavierStokesHermiteFarisLavine
import Definitions.Def_ChapterNavierStokesIkebeKato
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.basisState_coe (κ c : ℝ) (n m : ℕ) :
    ((basisState κ c n : L2I ℕ) : ℕ → ℂ) m = if m = n then 1 else 0 := by sorry

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