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Theorems · Theorem · logic and foundations

Finite.card_eq

∀ {α : Type u_1} {β : Type u_2} [Finite α] [Finite β], Nat.card α = Nat.card β ↔ Nonempty (α ≃ β)
Defined in
Mathlib.SetTheory.Cardinal.NatCard
Cited by
4 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FiniteFinite
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Around this declaration

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

SubMulAction.ofFixingSubgroup.isMultiplyPretransitive · cited by 4ofFixingSubgroup.isMultip…SubAddAction.ofFixingAddSubgroup.isMultiplyPretransitive · cited by 3ofFixingAddSubgroup.isMul…SubMulAction.ofFixingSubgroup.append_left · cited by 1ofFixingSubgroup.append_l…SubAddAction.ofFixingAddSubgroup.append_left · cited by 1ofFixingAddSubgroup.appen…Equiv · cited by 8337EquivFintype · cited by 7736FintypeFinite · cited by 3029FiniteNat.card · cited by 844Nat.cardFintype.ofFinite · cited by 255Fintype.ofFiniteNat.card_eq_fintype_card · cited by 200Nat.card_eq_fintype_cardFinite.card_eqCITED BYCITES

Cites6

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

Cited by4

Results whose statement or proof uses this declaration.