Theorems · Theorem · logic and foundations
Set.ncard_eq_zero
∀ {α : Type u_1} {s : Set α}, autoParam s.Finite Set.ncard_eq_zero._auto_1 → (s.ncard = 0 ↔ s = ∅)- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ENatproof · cited by 4,985
- Nat.cast_zeroproof · cited by 1,870
- Set.Finitestatement and proof · cited by 1,814
- Set.ncardstatement · cited by 344
- Set.encardproof · cited by 327
- Nat.cast_injproof · cited by 70
- Set.Finite.cast_ncard_eqproof · cited by 28
- Set.encard_eq_zeroproof · cited by 12
Cited by7
Results whose statement or proof uses this declaration.
- Set.ncard_emptyproof · cited by 14
- Set.ncard_posproof · cited by 11
- Set.eq_univ_iff_ncardproof · cited by 4
- MulAction.IsMultiplyPretransitive.index_of_fixingSubgroup_mulproof · cited by 2
- Set.ncard_union_eq_iffproof · cited by 2
- Submodule.spanFinrank_eq_zero_iff_eq_botproof · cited by 1
- Set.powersetCard.eq_empty_iffproof · cited by 0