`BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp` (b₁ b₂ : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : boolFlip b₁ (boolFlip b₂ x) = boolFlip (fun k => xor (b₁ k) (b₂ k))

Proved

BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp

by leonardopedro · Oct 5, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFreeFieldBornSignAction.

BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp (b₁ b₂ : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) : boolFlip b₁ (boolFlip b₂ x) = boolFlip (fun k => xor (b₁ k) (b₂ k)) x

Formalization note: Lean 4 identifier BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp.

Preamble

-- Generated from ChapterFreeFieldBornSignAction.lean — theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp
import Definitions.Def_ChapterFreeFieldBorn
import Definitions.Def_ChapterFreeFieldBornSignGauge
import Mathlib
import Definitions.Def_ChapterFreeFieldBornSignAction
open BookProof.ChapterFreeFieldBornSignAction

variable {n : ℕ}


open MeasureTheory
open BookProof.ChapterFreeFieldBorn
open BookProof.ChapterFreeFieldBornSignGauge

Formal statement

theorem BookProof.ChapterFreeFieldBornSignAction.boolFlip_comp (b₁ b₂ : Fin n → Bool) (x : EuclideanSpace ℝ (Fin n)) :
    boolFlip b₁ (boolFlip b₂ x) = boolFlip (fun k => xor (b₁ k) (b₂ k)) x := by sorry

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