Theorems · Theorem · combinatorics
Finset.card_eq_zero
∀ {α : Type u_1} {s : Finset α}, s.card = 0 ↔ s = ∅- Defined in
- Mathlib.Data.Finset.Card
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, 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
- Multiset.card_eq_zeroproof · cited by 13
- Finset.val_eq_zeroproof · cited by 12
Cited by34
Results whose statement or proof uses this declaration.
- Fintype.card_eq_zero_iffproof · cited by 14
- MeasureTheory.Measure.haar.index_posproof · cited by 5
- Finset.card_ne_zeroproof · cited by 5
- MeasureTheory.Measure.haar.addIndex_posproof · cited by 5
- Finset.card_ne_zero_of_memproof · cited by 4
- Equiv.Perm.card_support_eq_zeroproof · cited by 3
- hammingDist_selfproof · cited by 2
- Equiv.Perm.card_of_cycleType_eq_zero_iffproof · cited by 2
- DividedPowers.dpow_sum'proof · cited by 2
- AddGroup.rank_eq_zero_iffproof · cited by 2
- card_addOrderOf_eq_totient_aux₂proof · cited by 2
- Group.rank_eq_zero_iffproof · cited by 2