`BookProof.ChapterPauliFundamental.sel_hi_insert` : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∉ T → sel (hi μ (insert μ T)) = μ :: sel (hi μ T)

Proved

BookProof.ChapterPauliFundamental.sel_hi_insert

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliFundamental.

BookProof.ChapterPauliFundamental.sel_hi_insert : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∉ T → sel (hi μ (insert μ T)) = μ :: sel (hi μ T)

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

Preamble

-- Generated from ChapterPauliFundamental.lean — theorem BookProof.ChapterPauliFundamental.sel_hi_insert
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_insert : ∀ (μ : Fin 4) (T : Finset (Fin 4)), μ ∉ T →
    sel (hi μ (insert μ T)) = μ :: sel (hi μ T) := by sorry

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