Theorems · Theorem · logic and foundations
Set.ncard_empty
∀ (α : Type u_3), ∅.ncard = 0
- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 100 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.
- Setstatement · cited by 53,352
- Set.ncardstatement · cited by 344
- Set.toFiniteproof · cited by 174
- Set.ncard_eq_zeroproof · cited by 7
Cited by14
Results whose statement or proof uses this declaration.
- Set.nonempty_of_ncard_ne_zeroproof · cited by 5
- MulAction.IsBlock.eq_univ_of_card_ltproof · cited by 3
- Finset.set_ncard_biUnion_leproof · cited by 2
- ProbabilityTheory.setBernoulli_emptyproof · cited by 2
- Set.exists_subset_card_eqproof · cited by 2
- SimpleGraph.IsTutteViolator.emptyproof · cited by 1
- AddAction.IsBlock.eq_univ_of_card_ltproof · cited by 1
- Equiv.Perm.isCoatom_stabilizer_of_ncard_lt_ncard_complproof · cited by 1
- ProbabilityTheory.binomial_zeroproof · cited by 0
- MulAction.IsBlock.subsingleton_of_card_ltproof · cited by 0
- Set.ncard_le_one_iff_eqproof · cited by 0
- ProbabilityTheory.map_cast_binomial_zeroproof · cited by 0