Theorems · Theorem · logic and foundations
Nat.finite_of_card_ne_zero
∀ {α : Type u_1}, Nat.card α ≠ 0 → Finite α- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 95 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 · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- Nat.card_ne_zeroproof · cited by 6
Cited by33
Results whose statement or proof uses this declaration.
- Subgroup.eq_top_of_card_eqproof · cited by 4
- Subgroup.eq_bot_or_eq_top_of_prime_cardproof · cited by 3
- isCyclic_of_prime_cardproof · cited by 3
- MulAction.IsPreprimitive.is_two_motive_of_is_motiveproof · cited by 2
- AddSubgroup.eq_bot_or_eq_top_of_prime_cardproof · cited by 2
- Subgroup.exists_right_complement'_of_coprimeproof · cited by 2
- Ideal.absNorm_ne_zero_iffproof · cited by 2
- Set.powersetCard.nontrivial'proof · cited by 1
- IsPGroup.card_center_eq_prime_powproof · cited by 1
- AddSubgroup.eq_top_of_card_eqproof · cited by 1
- isSimpleAddGroup_of_prime_cardproof · cited by 1
- isSimpleGroup_of_prime_cardproof · cited by 1