`BookProof.ChapterPauliFundamental.sel_hi_mem` : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∈ T → sel (hi μ T) = μ :: sel (hi μ (T.erase μ))

Proved

BookProof.ChapterPauliFundamental.sel_hi_mem

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.sel_hi_mem : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∈ T → sel (hi μ T) = μ :: sel (hi μ (T.erase μ))

Formalization note: Lean 4 identifier BookProof.ChapterPauliFundamental.sel_hi_mem.

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.sel_hi_mem
import Definitions.Def_ChapterA3
import Definitions.Def_ChapterGammaCommutant
import Mathlib
import Definitions.Def_ChapterPauliFundamental
open BookProof.ChapterPauliFundamental


open Matrix Finset


open BookProof.ChapterA3 BookProof.ChapterGammaCommutant

variable {A : Fin 4 → M4}

Formal statement

theorem BookProof.ChapterPauliFundamental.sel_hi_mem : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∈ T →
    sel (hi μ T) = μ :: sel (hi μ (T.erase μ)) := by sorry

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