Theorems · Inductive type · combinatorics
Infinite
Sort u_3 → Prop
A type is said to be infinite if it is not finite. Note that Infinite α is equivalent to
IsEmpty (Fintype α) or IsEmpty (Finite α).
- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 352 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by375
Results whose statement or proof uses this declaration.
- finite_or_infinitestatement · cited by 50
- Nat.card_eq_zero_of_infinitestatement and proof · cited by 46
- Cardinal.aleph0_le_mkstatement and proof · cited by 32
- Filter.hyperfilterstatement and proof · cited by 30
- Cardinal.mk_eq_aleph0statement and proof · cited by 20
- Set.Infinite.to_subtypestatement · cited by 19
- Cardinal.lt_aleph0proof · cited by 19
- Set.infinite_coe_iffstatement · cited by 16
- fintypeOrInfinitestatement and proof · cited by 14
- orderOf_dvd_natCardproof · cited by 14
- Set.infinite_univstatement and proof · cited by 13
- Infinite.natEmbeddingstatement and proof · cited by 12
Showing the 200 most cited of 375.