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Theorems · Theorem · logic and foundations

Set.ncard_le_one_iff_subset_singleton

∀ {α : Type u_1} {s : Set α} [Nonempty α],
  autoParam s.Finite Set.ncard_le_one_iff_subset_singleton._auto_1 → (s.ncard ≤ 1 ↔ ∃ x, s ⊆ {x})
Defined in
Mathlib.Data.Set.Card
Cited by
1 results in Mathlib
Foundations
Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
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Around this declaration

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

Function.Surjective.card_le_card_add_one_iff · cited by 1Surjective.card_le_card_a…Set · cited by 53352SetSet.Finite · cited by 1814Set.FiniteSet.ncard · cited by 344Set.ncardFinset.coe_singleton · cited by 145Finset.coe_singletonSet.ncard_eq_toFinset_card · cited by 21Set.ncard_eq_toFinset_cardSet.ncard_le_one_iff_subset_s…CITED BYCITES

Cites5

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Cited by1

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