`BookProof.ChapterA3q.projMixed_spinGenDiag_comm` {N : ℕ} (μ ν : Fin 4) : projMixed N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projMixed N

Proved

BookProof.ChapterA3q.projMixed_spinGenDiag_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3q.

BookProof.ChapterA3q.projMixed_spinGenDiag_comm {N : ℕ} (μ ν : Fin 4) : projMixed N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projMixed N

Formalization note: Lean 4 identifier BookProof.ChapterA3q.projMixed_spinGenDiag_comm.

Preamble

-- Generated from ChapterA3q.lean — theorem BookProof.ChapterA3q.projMixed_spinGenDiag_comm
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterA3o
import Definitions.Def_ChapterA3p
import Mathlib
import Definitions.Def_ChapterA3q
import Definitions.Def_ChapterA3j
import Definitions.Def_ChapterA3n
open BookProof.ChapterA3j
open BookProof.ChapterA3n
open BookProof.ChapterA3q


open Matrix
open scoped BigOperators


open BookProof.ChapterA3 BookProof.ChapterA3j BookProof.ChapterA3n BookProof.ChapterA3o
open BookProof.ChapterA3p

Formal statement

theorem BookProof.ChapterA3q.projMixed_spinGenDiag_comm {N : ℕ} (μ ν : Fin 4) :
    projMixed N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projMixed N := by sorry

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