`BookProof.ChapterG.swap_mem_gaugeGroup` {X Y : Type*} [DecidableEq X] {π : X → Y} {x x' : X} (h : π x = π x') : Equiv.swap x x' ∈ gaugeGroup π

Proved

BookProof.ChapterG.swap_mem_gaugeGroup

by leonardopedro · Oct 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG.

BookProof.ChapterG.swap_mem_gaugeGroup {X Y : Type*} [DecidableEq X] {π : X → Y} {x x' : X} (h : π x = π x') : Equiv.swap x x' ∈ gaugeGroup π

Formalization note: Lean 4 identifier BookProof.ChapterG.swap_mem_gaugeGroup.

Preamble

-- Generated from ChapterG.lean — theorem BookProof.ChapterG.swap_mem_gaugeGroup
import Mathlib
import Definitions.Def_ChapterG
open BookProof.ChapterG


open scoped ComplexConjugate InnerProductSpace Matrix

Formal statement

theorem BookProof.ChapterG.swap_mem_gaugeGroup {X Y : Type*} [DecidableEq X] {π : X → Y}
    {x x' : X} (h : π x = π x') :
    Equiv.swap x x' ∈ gaugeGroup π := by sorry

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