Theorems · Theorem · combinatorics
not_finite_iff_infinite
∀ {α : Sort u_1}, ¬Finite α ↔ Infinite α- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement · cited by 3,029
- Infinitestatement and proof · cited by 352
- Infinite.not_finiteproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- finite_or_infiniteproof · cited by 50
- Set.infinite_coe_iffproof · cited by 16
- Cardinal.infinite_iffproof · cited by 12
- not_infinite_iff_finiteproof · cited by 3
- Set.infinite_univ_iffproof · cited by 3
- Equiv.infinite_iffproof · cited by 2
- ConnectedComponents.exists_fun_isClopen_of_infiniteproof · cited by 1
- Nat.card_eqproof · cited by 1