Theorems · Theorem · logic and foundations
Set.encard_singleton
∀ {α : Type u_1} (e : α), {e}.encard = 1- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENatstatement and proof · cited by 4,985
- Set.encardstatement · cited by 327
- ENat.card_eq_coe_fintype_cardproof · cited by 15
- Nat.cast_eq_oneproof · cited by 6
- Set.card_singletonproof · cited by 1
Cited by26
Results whose statement or proof uses this declaration.
- Set.encard_insert_of_notMemproof · cited by 17
- Set.ncard_singletonproof · cited by 8
- Set.encard_eq_oneproof · cited by 6
- Metric.coveringNumber_eq_one_of_ediam_leproof · cited by 3
- Matroid.IsNonloop.eRk_eqproof · cited by 3
- Set.encard_pairproof · cited by 3
- Matroid.IsBase.exchange_isBase_of_indepproof · cited by 3
- Set.powersetCard.exists_mem_notMemproof · cited by 2
- Set.encard_eq_threeproof · cited by 2
- Set.encard_insert_leproof · cited by 1
- Set.encard_ne_add_oneproof · cited by 1
- SimpleGraph.IsBridge.not_isEdgeReachable_twoproof · cited by 1