Theorems · Theorem · combinatorics
Set.finite_or_infinite
∀ {α : Type u} (s : Set α), s.Finite ∨ s.InfiniteSee also finite_or_infinite, fintypeOrInfinite.
- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Finitestatement and proof · cited by 1,814
- Set.Infinitestatement · cited by 263
- emproof · cited by 115
Cited by23
Results whose statement or proof uses this declaration.
- Nat.nth_memproof · cited by 9
- Set.ncard_union_leproof · cited by 4
- Set.finite_of_ncard_ne_zeroproof · cited by 4
- Nat.nth_lt_nth'proof · cited by 4
- Set.ncard_sdiffproof · cited by 4
- Nat.exists_lt_card_nth_eqproof · cited by 3
- Nat.card_image_of_injOnproof · cited by 3
- Real.infinite_rat_abs_sub_lt_one_div_den_sq_of_irrationalproof · cited by 2
- Matroid.rankFinite_or_rankInfiniteproof · cited by 2
- Set.ncard_le_ncard_sdiff_add_ncardproof · cited by 2
- Set.ncard_sdiff_singleton_leproof · cited by 1
- Matroid.indep_iff_eRk_eq_encardproof · cited by 1