`BookProof.ChapterScaledDotProduct.flipEquiv_apply_self` (i : Fin d) (x : Fin d → Bool) : (flipEquiv i x) i = !(x i)

Proved

BookProof.ChapterScaledDotProduct.flipEquiv_apply_self

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterScaledDotProduct.

BookProof.ChapterScaledDotProduct.flipEquiv_apply_self (i : Fin d) (x : Fin d → Bool) : (flipEquiv i x) i = !(x i)

Formalization note: Lean 4 identifier BookProof.ChapterScaledDotProduct.flipEquiv_apply_self.

Preamble

-- Generated from ChapterScaledDotProduct.lean — theorem BookProof.ChapterScaledDotProduct.flipEquiv_apply_self
import Definitions.Def_ChapterSoftmaxSharpness
import Mathlib
import Definitions.Def_ChapterScaledDotProduct
open BookProof.ChapterScaledDotProduct


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxSharpness

variable {d : ℕ}

Formal statement

theorem BookProof.ChapterScaledDotProduct.flipEquiv_apply_self (i : Fin d) (x : Fin d → Bool) :
    (flipEquiv i x) i = !(x i) := by sorry

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