Theorems · Theorem · logic and foundations
Set.Infinite.encard_eq
∀ {α : Type u_1} {s : Set α}, s.Infinite → s.encard = ⊤- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 6 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.
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
- Set.Elemproof · cited by 7,166
- ENatstatement and proof · cited by 4,985
- Infiniteproof · cited by 352
- Set.encardstatement · cited by 327
- Set.Infinitestatement and proof · cited by 263
- Set.Infinite.to_subtypeproof · cited by 19
- ENat.card_eq_top_of_infiniteproof · cited by 11
Cited by6
Results whose statement or proof uses this declaration.
- Set.encard_lt_top_iffproof · cited by 5
- Set.ncard_sdiff_singleton_of_memproof · cited by 2
- Submodule.spanRank_toENat_eq_iInf_finset_cardproof · cited by 2
- Set.eq_empty_or_encard_eq_top_or_encard_sdiff_singleton_ltproof · cited by 1
- Set.Finite.encard_biUnionproof · cited by 1
- Matroid.indep_iff_eRk_eq_encardproof · cited by 1