`BookProof.ChapterA3n.projSym_spinGenDiag_comm` {N : ℕ} (μ ν : Fin 4) : projSym N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projSym N

Proved

BookProof.ChapterA3n.projSym_spinGenDiag_comm

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3n.

BookProof.ChapterA3n.projSym_spinGenDiag_comm {N : ℕ} (μ ν : Fin 4) : projSym N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projSym N

Formalization note: Lean 4 identifier BookProof.ChapterA3n.projSym_spinGenDiag_comm.

Preamble

-- Generated from ChapterA3n.lean — theorem BookProof.ChapterA3n.projSym_spinGenDiag_comm
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterA3n
import Definitions.Def_ChapterA3j
import Definitions.Def_ChapterA3l
open BookProof.ChapterA3j
open BookProof.ChapterA3l
open BookProof.ChapterA3n


open Matrix
open scoped BigOperators


open BookProof.ChapterA3 BookProof.ChapterA3j

Formal statement

theorem BookProof.ChapterA3n.projSym_spinGenDiag_comm {N : ℕ} (μ ν : Fin 4) :
    projSym N * diagGen (spinGen μ ν) = diagGen (spinGen μ ν) * projSym N := by sorry

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