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`BookProof.ChapterA4e.spatialOp_swaps_neg` (j : Fin 3) : projNeg * spatialOp j = spatialOp j * projPos

Proved
BookProof.ChapterA4e.spatialOp_swaps_neg

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA4e.

BookProof.ChapterA4e.spatialOp_swaps_neg (j : Fin 3) : projNeg * spatialOp j = spatialOp j * projPos

Formalization note: Lean 4 identifier BookProof.ChapterA4e.spatialOp_swaps_neg.

Preamble
-- Generated from ChapterA4e.lean — theorem BookProof.ChapterA4e.spatialOp_swaps_neg
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA5
import Mathlib
import Definitions.Def_ChapterA4e
open BookProof.ChapterA4e


open Matrix


open BookProof.ChapterA3 BookProof.ChapterA5
Formal statement
theorem BookProof.ChapterA4e.spatialOp_swaps_neg (j : Fin 3) :
    projNeg * spatialOp j = spatialOp j * projPos := by sorry

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