Theorems · Theorem · order theory
Set.finite_union
∀ {α : Type u} {s t : Set α}, (s ∪ t).Finite ↔ s.Finite ∧ t.Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Finitestatement and proof · cited by 1,814
- Set.Finite.subsetproof · cited by 285
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- Set.Finite.unionproof · cited by 74
Cited by4
Results whose statement or proof uses this declaration.
- TopologicalSpace.vietoris.isTopologicalBasisproof · cited by 2
- SimpleGraph.IsClique.even_iff_exists_isMatchingproof · cited by 1
- Set.card_union_leproof · cited by 1
- Set.exists_union_disjoint_cardinal_eq_iffproof · cited by 0