`BookProof.ChapterAttentionRetrieval.card_erase_cast` (j : Fin m) : ((Finset.univ.erase j).card : ℝ) = (m : ℝ) - 1

Proved

BookProof.ChapterAttentionRetrieval.card_erase_cast

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAttentionRetrieval.

BookProof.ChapterAttentionRetrieval.card_erase_cast (j : Fin m) : ((Finset.univ.erase j).card : ℝ) = (m : ℝ) - 1

Formalization note: Lean 4 identifier BookProof.ChapterAttentionRetrieval.card_erase_cast.

Preamble

-- Generated from ChapterAttentionRetrieval.lean — theorem BookProof.ChapterAttentionRetrieval.card_erase_cast
import Definitions.Def_ChapterSoftmaxSharpness
import Definitions.Def_ChapterSoftmaxOrder
import Mathlib
import Definitions.Def_ChapterAttentionRetrieval
open BookProof.ChapterAttentionRetrieval


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness BookProof.ChapterSoftmaxOrder

variable {m n : ℕ} {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]

Formal statement

theorem BookProof.ChapterAttentionRetrieval.card_erase_cast (j : Fin m) :
    ((Finset.univ.erase j).card : ℝ) = (m : ℝ) - 1 := by sorry

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