Theorems · Theorem · logic and foundations
Set.encard_eq_zero
∀ {α : Type u_1} {s : Set α}, s.encard = 0 ↔ s = ∅- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Set.encardstatement · cited by 327
- Set.eq_empty_iff_forall_notMemproof · cited by 42
- ENat.card_eq_zero_iff_emptyproof · cited by 3
- isEmpty_subtypeproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Set.encard_emptyproof · cited by 17
- Set.ncard_eq_zeroproof · cited by 7
- Set.nonempty_of_encard_ne_zeroproof · cited by 5
- Set.Finite.eq_of_subset_of_encard_le'proof · cited by 4
- Set.one_le_encard_iff_nonemptyproof · cited by 3
- Matroid.IsBase.exchange_isBase_of_indepproof · cited by 3
- AddAction.is_zero_preprimitiveproof · cited by 2
- Set.encard_le_one_iff_eqproof · cited by 2
- Matroid.eRank_eq_zero_iffproof · cited by 2
- Matroid.eRk_eq_zero_iff'proof · cited by 1
- Set.encard_ne_zeroproof · cited by 1
- AddAction.is_zero_preprimitive_iffproof · cited by 0