Theorems · Theorem · order theory
Set.Finite.union
∀ {α : Type u} {s t : Set α}, s.Finite → t.Finite → (s ∪ t).Finite- Defined in
- Mathlib.Data.Set.Finite.Basic
- Cited by
- 74 results in Mathlib
- Foundations
- Depth 63 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 and proof · cited by 53,352
- Set.Finitestatement and proof · cited by 1,814
- Set.toFiniteproof · cited by 174
Cited by75
Results whose statement or proof uses this declaration.
- Filter.cofiniteproof · cited by 251
- Set.Finite.insertproof · cited by 11
- Submodule.FG.supproof · cited by 9
- Set.ncard_union_eqproof · cited by 6
- AddSubgroup.fg_iff_addSubmonoid_fgproof · cited by 6
- TopologicalSpace.isTopologicalBasis_of_subbasisproof · cited by 6
- Subgroup.fg_iff_submonoid_fgproof · cited by 5
- finprod_le_finprodproof · cited by 5
- FirstOrder.Language.Substructure.FG.supproof · cited by 5
- Set.ncard_union_add_ncard_interproof · cited by 4
- Set.finite_unionproof · cited by 4
- Set.Finite.of_sdiffproof · cited by 4