Theorems · Theorem · logic and foundations
Nat.card_pos
∀ {α : Type u_1} [Nonempty α] [Finite α], 0 < Nat.card α- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement · cited by 844
- Nat.card_pos_iffproof · cited by 6
Cited by36
Results whose statement or proof uses this declaration.
- Sylow.not_dvd_indexproof · cited by 9
- Subgroup.index_ne_zero_of_finiteproof · cited by 5
- Subgroup.eq_top_of_card_eqproof · cited by 4
- NumberField.Units.torsionOrder_posproof · cited by 4
- AddSubgroup.index_ne_zero_of_finiteproof · cited by 4
- MonoidHom.surjective_of_card_ker_le_divproof · cited by 2
- Submodule.finite_quotient_smulproof · cited by 2
- Height.mulHeight_eval_geproof · cited by 2
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- Height.mulHeight_linearMap_apply_leproof · cited by 2
- AlgHom.IsArithFrobAt.card_posproof · cited by 2
- Sylow.card_eq_multiplicityproof · cited by 2