Prove2Me

`BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero` (hd : 0 < d) (x : Fin d → ℝ) : ∑ i, (x i - mean x) = 0

Proved
BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterLayerNorm.

BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero (hd : 0 < d) (x : Fin d → ℝ) : ∑ i, (x i - mean x) = 0

Formalization note: Lean 4 identifier BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero.

Preamble
-- Generated from ChapterLayerNorm.lean — theorem BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterLayerNorm
import Definitions.Def_ChapterTotalVariance
open ChapterTotalVariance
open BookProof.ChapterLayerNorm


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {d : ℕ}
Formal statement
theorem BookProof.ChapterLayerNorm.sum_sub_mean_eq_zero (hd : 0 < d) (x : Fin d → ℝ) : ∑ i, (x i - mean x) = 0 := by sorry

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