Theorems · Theorem · combinatorics
set_fintype_card_eq_univ_iff
∀ {α : Type u_1} [inst : Fintype α] (s : Set α) [inst_1 : Fintype ↑s], Fintype.card ↑s = Fintype.card α ↔ s = Set.univ- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetproof · cited by 13,712
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- Set.univstatement and proof · cited by 3,945
- Fintype.cardstatement and proof · cited by 1,386
- Set.toFinsetproof · cited by 217
- Set.toFinset_cardproof · cited by 63
- Set.toFinset_univproof · cited by 10
- Finset.card_eq_iff_eq_univproof · cited by 6
- Set.toFinset_injproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- commProb_eq_one_iffproof · cited by 1
- SimpleGraph.odd_ncard_oddComponentsproof · cited by 1
- SimpleGraph.copyCount_botproof · cited by 0