Theorems · Theorem · combinatorics
Finset.Nonempty.card_pos
∀ {α : Type u_1} {s : Finset α}, s.Nonempty → 0 < s.cardAlias of the reverse direction of Finset.card_pos.
- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 55 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.
Cites4
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
- Finset.cardstatement · cited by 2,327
- Finset.Nonemptystatement · cited by 1,001
- Finset.card_posproof · cited by 53
Cited by55
Results whose statement or proof uses this declaration.
- Finset.mulConst_mul_cardproof · cited by 4
- Lagrange.degree_interpolate_ltproof · cited by 4
- Finset.divConst_mul_cardproof · cited by 4
- Finset.subConst_mul_cardproof · cited by 4
- Finset.addConst_mul_cardproof · cited by 4
- Lagrange.sum_basisproof · cited by 3
- sum_div_card_sq_le_sum_sq_div_cardproof · cited by 3
- Finset.addEnergy_posproof · cited by 2
- Finset.ruzsa_covering_addproof · cited by 2
- Finset.ruzsa_covering_mulproof · cited by 2
- Equiv.Perm.IsCycleOn.exists_pow_eqproof · cited by 2
- Finset.ruzsa_triangle_inequality_add_add_addproof · cited by 2