`BookProof.ChapterG3.faithful_remnant_nontrivial` {G Y : Type*} [Group G] [MulAction G Y] [FaithfulSMul G Y] [Nontrivial G] : ∃ (g : G) (y : Y), g • y ≠ y

Proved

BookProof.ChapterG3.faithful_remnant_nontrivial

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterG3.

BookProof.ChapterG3.faithful_remnant_nontrivial {G Y : Type*} [Group G] [MulAction G Y] [FaithfulSMul G Y] [Nontrivial G] : ∃ (g : G) (y : Y), g • y ≠ y

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

Preamble

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


open MeasureTheory
open scoped ENNReal



variable {X : Type*}

Formal statement

theorem BookProof.ChapterG3.faithful_remnant_nontrivial {G Y : Type*} [Group G] [MulAction G Y]
    [FaithfulSMul G Y] [Nontrivial G] : ∃ (g : G) (y : Y), g • y ≠ y := by sorry

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