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Theorems · Theorem · group theory

Set.finite_smul_set

∀ {G : Type u_1} {α : Type u_2} [inst : Group G] [inst_1 : MulAction G α] {a : G} {s : Set α}, (a • s).Finite ↔ s.Finite
Defined in
Mathlib.Algebra.Group.Action.Pointwise.Set.Finite
Cited by
1 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupMulAction
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.Finite.of_smul_set · cited by 0Finite.of_smul_setSet · cited by 53352SetGroup · cited by 6238GroupSet.Finite · cited by 1814Set.FiniteMulAction · cited by 1294MulActionSet.smulSet · cited by 608Set.smulSetFunction.Injective.injOn · cited by 280Injective.injOnMulAction.injective · cited by 24MulAction.injectiveSet.finite_image_iff · cited by 16Set.finite_image_iffSet.finite_smul_setCITED BYCITES

Cites8

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Cited by1

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