Theorems · Theorem · logic and foundations
IsSemilinearSet.union
∀ {M : Type u_1} [inst : AddCommMonoid M] {s₁ s₂ : Set M},
IsSemilinearSet s₁ → IsSemilinearSet s₂ → IsSemilinearSet (s₁ ∪ s₂)Semilinear sets are closed under union.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Set.Finiteproof · cited by 1,814
- Set.sUnionproof · cited by 392
- Set.Finite.unionproof · cited by 74
- Set.mem_unionproof · cited by 47
- IsSemilinearSetstatement and proof · cited by 44
- IsLinearSetproof · cited by 28
- Set.sUnion_unionproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- IsSemilinearSet.sUnionproof · cited by 2
- IsLinearSet.closureproof · cited by 1
- Nat.isSemilinearSet_iff_ultimately_periodicproof · cited by 1