Theorems · Theorem · combinatorics
Finset.card_lt_iff_ne_univ
∀ {α : Type u_1} [inst : Fintype α] (s : Finset α), s.card < Fintype.card α ↔ s ≠ Finset.univ- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Finset.univstatement · cited by 3,473
- Finset.cardstatement · cited by 2,327
- Fintype.cardstatement · cited by 1,386
- LE.le.lt_iff_neproof · cited by 34
- Finset.card_le_univproof · cited by 32
- Finset.card_eq_iff_eq_univproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- AhlswedeZhang.supSum_singletonproof · cited by 1
- HallMarriageTheorem.hall_hard_inductive_step_Bproof · cited by 1
- Finset.card_compl_lt_iff_nonemptyproof · cited by 1