`BookProof.ChapterG.gaugeOrbit_eq_fiber` {X Y : Type*} (π : X → Y) (x : X) : MulAction.orbit (gaugeGroup π) x = π ⁻¹' {π x}

Proved

BookProof.ChapterG.gaugeOrbit_eq_fiber

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG.

BookProof.ChapterG.gaugeOrbit_eq_fiber {X Y : Type*} (π : X → Y) (x : X) : MulAction.orbit (gaugeGroup π) x = π ⁻¹' {π x}

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

Preamble

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


open scoped ComplexConjugate InnerProductSpace Matrix

Formal statement

theorem BookProof.ChapterG.gaugeOrbit_eq_fiber {X Y : Type*} (π : X → Y) (x : X) :
    MulAction.orbit (gaugeGroup π) x = π ⁻¹' {π x} := by sorry

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