`BookProof.ChapterGaugeParametrization.orbit_eq_fiber` (π : X → Y) (x : X) : MulAction.orbit (fiberGauge π) x = π ⁻¹' {π x}

Proved

BookProof.ChapterGaugeParametrization.orbit_eq_fiber

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterGaugeParametrization.

BookProof.ChapterGaugeParametrization.orbit_eq_fiber (π : X → Y) (x : X) : MulAction.orbit (fiberGauge π) x = π ⁻¹' {π x}

Formalization note: Lean 4 identifier BookProof.ChapterGaugeParametrization.orbit_eq_fiber.

Preamble

-- Generated from ChapterGaugeParametrization.lean — theorem BookProof.ChapterGaugeParametrization.orbit_eq_fiber
import Definitions.Def_ChapterGaugeIncompleteFixing
import Mathlib
import Definitions.Def_ChapterGaugeParametrization
open BookProof.ChapterGaugeParametrization



open BookProof.ChapterGaugeIncompleteFixing

variable {X Y : Type*}

Formal statement

theorem BookProof.ChapterGaugeParametrization.orbit_eq_fiber (π : X → Y) (x : X) :
    MulAction.orbit (fiberGauge π) x = π ⁻¹' {π x} := by sorry

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