Theorems · Theorem · combinatorics
Fintype.card_pos_iff
∀ {α : Type u_1} [inst : Fintype α], 0 < Fintype.card α ↔ Nonempty α- Defined in
- Mathlib.Data.Fintype.Card
- Cited by
- 31 results in Mathlib
- Foundations
- Depth 63 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- not_iff_commproof · cited by 32
- not_nonempty_iffproof · cited by 20
- Fintype.card_eq_zero_iffproof · cited by 14
Cited by31
Results whose statement or proof uses this declaration.
- Fintype.card_posproof · cited by 31
- Finite.card_pos_iffproof · cited by 3
- Configuration.ProjectivePlane.lineCount_eqproof · cited by 3
- card_orderOf_eq_totient_aux₂proof · cited by 2
- ClassGroup.normBound_posproof · cited by 2
- char_dvd_card_solutions_of_sum_ltproof · cited by 2
- Configuration.HasLines.card_leproof · cited by 2
- card_addOrderOf_eq_totient_aux₂proof · cited by 2
- Matrix.inv_zeroproof · cited by 2
- SimpleGraph.card_le_chromaticNumber_iff_forall_surjectiveproof · cited by 2
- Matrix.charpoly_of_card_eq_twoproof · cited by 2
- AffineSubspace.card_pos_of_affineSpan_eq_topproof · cited by 1