Theorems · Theorem · combinatorics
not_infinite_iff_finite
∀ {α : Sort u_1}, ¬Infinite α ↔ Finite α- Defined in
- Mathlib.Data.Finite.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 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.
- Finitestatement · cited by 3,029
- Infinitestatement · cited by 352
- Iff.not_rightproof · cited by 20
- not_finite_iff_infiniteproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Finite.not_infiniteproof · cited by 2
- Finite.of_not_infiniteproof · cited by 2
- AddSubgroup.index_ne_zero_iff_finiteproof · cited by 1