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Theorems · Theorem · logic and foundations

Nat.card_unique

∀ {α : Type u_1} [Nonempty α] [Subsingleton α], Nat.card α = 1
Defined in
Mathlib.SetTheory.Cardinal.Finite
Cited by
8 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonemptySubsingleton
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Around this declaration

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

Nat.card_units · cited by 6Nat.card_unitsProjectivization.card · cited by 3Projectivization.cardGroup.isCyclic_prod_iff · cited by 2Group.isCyclic_prod_iffIsPurelyInseparable.finSepDegree_eq_one · cited by 2IsPurelyInseparable.finSe…Ideal.card_norm_le_eq_card_norm_le_add_one · cited by 2Ideal.card_norm_le_eq_car…IsPGroup.of_subsingleton · cited by 2IsPGroup.of_subsingletonLinearMap.exists_mem_center_apply_eq_smul_of_forall_notLinearIndependent · cited by 1LinearMap.exists_mem_cent…AddGroup.isAddCyclic_prod_iff · cited by 0AddGroup.isAddCyclic_prod…Nat.card · cited by 844Nat.cardNat.card_uniqueCITED BYCITES

Cites1

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

Cited by8

Results whose statement or proof uses this declaration.