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Theorems · Theorem · group theory

Set.finite_inv

∀ {α : Type u_2} [inst : InvolutiveInv α] {s : Set α}, s⁻¹.Finite ↔ s.Finite
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Finite
Cited by
3 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
InvolutiveInv
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Around this declaration

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

Set.Finite.inv · cited by 2Finite.invSet.infinite_inv · cited by 0Set.infinite_invSet.Finite.of_inv · cited by 0Finite.of_invSet · cited by 53352SetSet.Finite · cited by 1814Set.FiniteFunction.Injective.injOn · cited by 280Injective.injOnSet.inv · cited by 132Set.invInvolutiveInv · cited by 102InvolutiveInvSet.image_inv_eq_inv · cited by 44Set.image_inv_eq_invinv_injective · cited by 17inv_injectiveSet.finite_image_iff · cited by 16Set.finite_image_iffSet.finite_invCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.