Theorems · Theorem · order theory
Set.finite_univ_iff
∀ {α : Type u}, Set.univ.Finite ↔ Finite α- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.univstatement · cited by 3,945
- Finitestatement · cited by 3,029
- Set.Finitestatement · cited by 1,814
- Equiv.Set.univproof · cited by 21
- Equiv.finite_iffproof · cited by 21
Cited by10
Results whose statement or proof uses this declaration.
- Finite.of_finite_univproof · cited by 4
- Set.infinite_univ_iffproof · cited by 3
- AddSubgroup.finiteIndex_of_leftCoset_cover_constproof · cited by 2
- Subgroup.finiteIndex_of_leftCoset_cover_constproof · cited by 2
- summable_const_iffproof · cited by 1
- Valued.integer.totallyBounded_iff_finite_residueFieldproof · cited by 1
- Set.Finite.finite_of_complproof · cited by 1
- Set.Finite.of_summable_constproof · cited by 1
- Algebra.QuasiFinite.finite_primeSpectrumproof · cited by 0
- JacobsonSpace.discreteTopologyproof · cited by 0