Theorems · Theorem · order theory
Set.finite_empty
∀ {α : Type u}, ∅.Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Set.Finitestatement · cited by 1,814
- Set.toFiniteproof · cited by 174
Cited by27
Results whose statement or proof uses this declaration.
- Filter.cofiniteproof · cited by 251
- Set.Finite.induction_onstatement and proof · cited by 39
- Set.Subsingleton.finiteproof · cited by 20
- Set.Infinite.nonemptyproof · cited by 6
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- finrank_eq_zero_of_basis_imp_not_finiteproof · cited by 2
- totallyBounded_emptyproof · cited by 2
- Set.seq_of_forall_finite_existsproof · cited by 2
- Set.Finite.induction_on_subsetstatement and proof · cited by 2
- Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integerproof · cited by 2
- UniformOnFun.isUniformEmbedding_toFun_finiteproof · cited by 2
- FirstOrder.Language.age.nonemptyproof · cited by 2