`BookProof.ChapterG3.free_remnant_moves_every_point` {G Y : Type*} [Group G] [MulAction G Y] (hfree : ∀ (g : G) (y : Y), g • y = y → g = 1) {g : G} (hg : g ≠ 1) (y : Y) : g • y ≠ y

Proved

BookProof.ChapterG3.free_remnant_moves_every_point

by leonardopedro · Oct 18, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG3.

BookProof.ChapterG3.free_remnant_moves_every_point {G Y : Type*} [Group G] [MulAction G Y] (hfree : ∀ (g : G) (y : Y), g • y = y → g = 1) {g : G} (hg : g ≠ 1) (y : Y) : g • y ≠ y

Formalization note: Lean 4 identifier BookProof.ChapterG3.free_remnant_moves_every_point.

Preamble

-- Generated from ChapterG3.lean — theorem BookProof.ChapterG3.free_remnant_moves_every_point
import Mathlib
import Definitions.Def_ChapterG3
open BookProof.ChapterG3


open MeasureTheory
open scoped ENNReal



variable {X : Type*}

Formal statement

theorem BookProof.ChapterG3.free_remnant_moves_every_point {G Y : Type*} [Group G] [MulAction G Y]
    (hfree : ∀ (g : G) (y : Y), g • y = y → g = 1) {g : G} (hg : g ≠ 1) (y : Y) :
    g • y ≠ y := by sorry

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