Theorems · Theorem · logic and foundations
Set.encard_eq_top_iff
∀ {α : Type u_1} {s : Set α}, s.encard = ⊤ ↔ s.Infinite- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.Finiteproof · cited by 1,814
- Set.encardstatement and proof · cited by 327
- Set.Infinitestatement · cited by 263
- lt_top_iff_ne_topproof · cited by 95
- Set.encard_lt_top_iffproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Set.Finite.cast_ncard_eqproof · cited by 28
- Set.infinite_iff_infinite_of_encard_eq_encardproof · cited by 1
- Matroid.eRk_eq_top_iffproof · cited by 1
- Set.encard_eq_topproof · cited by 1