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Theorems · Theorem · logic and foundations

Cardinal.mk_smul_set

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] (a : G) (s : Set α),
  Cardinal.mk ↑(a • s) = Cardinal.mk ↑s
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Card
Cited by
1 results in Mathlib
Foundations
Depth 22 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.encard_smul_set · cited by 1Set.encard_smul_setSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemGroup · cited by 6238GroupCardinal · cited by 2598CardinalMulAction · cited by 1294MulActionCardinal.mk · cited by 942Cardinal.mkSet.smulSet · cited by 608Set.smulSetFunction.Injective.injOn · cited by 280Injective.injOnMulAction.injective · cited by 24MulAction.injectiveCardinal.mk_image_eq_of_injOn · cited by 7Cardinal.mk_image_eq_of_i…Cardinal.mk_smul_setCITED BYCITES

Cites10

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Cited by1

Results whose statement or proof uses this declaration.