Theorems · Theorem · logic and foundations
Set.encard_lt_top_iff
∀ {α : Type u_1} {s : Set α}, s.encard < ⊤ ↔ s.Finite- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 96 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
- Top.topstatement and proof · cited by 9,680
- ENatstatement · cited by 4,985
- Set.Finitestatement and proof · cited by 1,814
- LT.lt.neproof · cited by 872
- Set.encardstatement and proof · cited by 327
- by_contraproof · cited by 60
- Set.Finite.encard_lt_topproof · cited by 10
- Set.Infinite.encard_eqproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Set.finite_of_encard_le_coeproof · cited by 5
- Set.encard_eq_top_iffproof · cited by 4
- Set.Finite.finite_of_encard_leproof · cited by 2
- Set.finite_iff_finite_of_encard_eq_encardproof · cited by 2
- Metric.exists_set_encard_eq_coveringNumberproof · cited by 0