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Theorems · Theorem · logic and foundations

Nat.card_eq_one_iff_unique

∀ {α : Type u_1}, Nat.card α = 1 ↔ Subsingleton α ∧ Nonempty α
Defined in
Mathlib.SetTheory.Cardinal.Finite
Cited by
15 results in Mathlib
Foundations
Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Subgroup.index_top · cited by 10Subgroup.index_topSubgroup.index_eq_one · cited by 9Subgroup.index_eq_oneAddSubgroup.index_top · cited by 9AddSubgroup.index_topAddSubgroup.index_eq_one · cited by 4AddSubgroup.index_eq_oneIsSimpleGroup.prime_card · cited by 3IsSimpleGroup.prime_cardSubgroup.exists_right_complement'_of_coprime · cited by 2Subgroup.exists_right_com…AddSubgroup.eq_bot_of_card_eq · cited by 2AddSubgroup.eq_bot_of_car…IsCyclic.normalizer_le_centralizer · cited by 2IsCyclic.normalizer_le_ce…IsSimpleAddGroup.prime_card · cited by 2IsSimpleAddGroup.prime_ca…Subgroup.eq_bot_of_card_eq · cited by 2Subgroup.eq_bot_of_card_eqField.finSepDegree_self · cited by 1Field.finSepDegree_selfIsCyclic.isComplement' · cited by 1IsCyclic.isComplement'isPurelyInseparable_iff_subsingleton_emb · cited by 1isPurelyInseparable_iff_s…IsPurelyInseparable.of_injective_comp_algebraMap · cited by 0IsPurelyInseparable.of_in…Nat.card_eq_one_iff_exists · cited by 0Nat.card_eq_one_iff_existsNat.card · cited by 844Nat.cardCardinal.toNat_eq_one_iff_unique · cited by 1Cardinal.toNat_eq_one_iff…Nat.card_eq_one_iff_uniqueCITED BYCITES

Cites2

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

Cited by15

Results whose statement or proof uses this declaration.