`BookProof.ChapterF8.featureHash_decodes` {k K : ℕ} (g : Fin k → Fin K) (hg : Function.Injective g) (y : Fin k → ℝ) (j : Fin k) : fockEmbed g y (Finsupp.single (g j) 1) = (y j : ℂ)

Proved

BookProof.ChapterF8.featureHash_decodes

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterF8.

BookProof.ChapterF8.featureHash_decodes {k K : ℕ} (g : Fin k → Fin K) (hg : Function.Injective g) (y : Fin k → ℝ) (j : Fin k) : fockEmbed g y (Finsupp.single (g j) 1) = (y j : ℂ)

Formalization note: Lean 4 identifier BookProof.ChapterF8.featureHash_decodes.

Preamble

-- Generated from ChapterF8.lean — theorem BookProof.ChapterF8.featureHash_decodes
import Mathlib
import Definitions.Def_ChapterF8
import Definitions.Def_ChapterNavierStokesFockManyMode
open BookProof.NavierStokesFlow.FockManyMode
open BookProof.ChapterF8


noncomputable section

open scoped BigOperators

Formal statement

theorem BookProof.ChapterF8.featureHash_decodes {k K : ℕ} (g : Fin k → Fin K) (hg : Function.Injective g)
    (y : Fin k → ℝ) (j : Fin k) :
    fockEmbed g y (Finsupp.single (g j) 1) = (y j : ℂ) := by sorry

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