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`BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights_one` {f : Fin m → Fin r} {p : Fin m → ℝ} (hp : ∑ x, p x = 1) : ∑ y, mergeWeights f p y = 1

Proved
BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights_one

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionCoarseGrain.

BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights_one {f : Fin m → Fin r} {p : Fin m → ℝ} (hp : ∑ x, p x = 1) : ∑ y, mergeWeights f p y = 1

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

Preamble
-- Generated from ChapterAttentionCoarseGrain.lean — theorem BookProof.ChapterAttentionCoarseGrain.sum_mergeWeights_one
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_one {f : Fin m → Fin r} {p : Fin m → ℝ} (hp : ∑ x, p x = 1) :
    ∑ y, mergeWeights f p y = 1 := by sorry

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