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`BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights` (f : Fin m → Fin r) (p : Fin m → ℝ) : ∑ y, mergeWeights f p y = ∑ x, p x

Proved
BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCoarseGrain.

BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights (f : Fin m → Fin r) (p : Fin m → ℝ) : ∑ y, mergeWeights f p y = ∑ x, p x

Formalization note: Lean 4 identifier BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights.

Preamble
-- Generated from ChapterAttentionCoarseGrain.lean — theorem BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights
import Definitions.Def_ChapterObservableExpectation
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterAttentionCoarseGrain
open BookProof.ChapterAttentionCoarseGrain


open scoped BigOperators

noncomputable section


open BookProof.ChapterObservableExpectation BookProof.ChapterSoftmaxSharpness

variable {m r : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
Formal statement
theorem BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights (f : Fin m → Fin r) (p : Fin m → ℝ) :
    ∑ y, mergeWeights f p y = ∑ x, p x := by sorry

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