Theorems · Theorem · logic and foundations
Set.encard_empty
∀ {α : Type u_1}, ∅.encard = 0- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 93 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
- ENatstatement · cited by 4,985
- Set.encardstatement · cited by 327
- Set.encard_eq_zeroproof · cited by 12
Cited by17
Results whose statement or proof uses this declaration.
- Set.Finite.encard_lt_topproof · cited by 10
- Set.exists_isChain_of_le_chainHeightproof · cited by 4
- Set.exists_subset_encard_eqproof · cited by 3
- SimpleGraph.vertexCoverNum_botproof · cited by 3
- Matroid.IsBase.exchange_isBase_of_indepproof · cited by 3
- Finset.set_encard_biUnion_leproof · cited by 2
- MulAction.is_one_preprimitive_iffproof · cited by 2
- MulAction.isMultiplyPreprimitive_succ_iff_ofStabilizerproof · cited by 2
- Set.encard_image_leproof · cited by 2
- SimpleGraph.vertexCoverNum_le_encard_edgeSetproof · cited by 1
- Matroid.eRk_loopyOnproof · cited by 1
- Metric.coveringNumber_emptyproof · cited by 1