Theorems · Theorem · combinatorics
Finset.one_lt_card_iff_nontrivial
∀ {α : Type u_1} {s : Finset α}, 1 < s.card ↔ s.Nontrivial- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 64 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.
- Finsetstatement and proof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Finset.cardstatement and proof · cited by 2,327
- not_ltproof · cited by 306
- not_iff_notproof · cited by 159
- Finset.Nontrivialstatement and proof · cited by 53
- not_nontrivial_iff_subsingletonproof · cited by 23
- Set.nontrivial_coe_sortproof · cited by 6
- Finset.coe_sort_coeproof · cited by 3
- Finset.card_le_one_iff_subsingleton_coeproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- TwoUniqueSums.of_addHomproof · cited by 1
- IsNonarchimedean.apply_sum_eq_of_ltproof · cited by 1
- TwoUniqueProds.of_mulHomproof · cited by 1
- SimpleGraph.isClique_map_finset_iffproof · cited by 1
- Set.powersetCard.coe_nontrivial_iffproof · cited by 0
- Nat.not_isPrimePow_iff_nontrivial_of_two_leproof · cited by 0