Theorems · Theorem · logic and foundations
IsSemilinearSet.iUnion
∀ {M : Type u_1} {ι : Type u_3} [inst : AddCommMonoid M] [Finite ι] {s : ι → Set M},
(∀ (i : ι), IsSemilinearSet (s i)) → IsSemilinearSet (⋃ i, s i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddCommMonoidstatement and proof · cited by 12,281
- Finitestatement and proof · cited by 3,029
- Set.iUnionstatement · cited by 2,483
- Set.finite_rangeproof · cited by 58
- IsSemilinearSetstatement and proof · cited by 44
- Set.sUnion_rangeproof · cited by 13
- IsSemilinearSet.sUnionproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsSemilinearSet.exists_fg_eq_subtypeValproof · cited by 1