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Theorems · Theorem · logic and foundations

IsSemilinearSet.sUnion

∀ {M : Type u_1} [inst : AddCommMonoid M] {S : Set (Set M)},
  S.Finite → (∀ s ∈ S, IsSemilinearSet s) → IsSemilinearSet (⋃₀ S)
Defined in
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs
Cited by
2 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsSemilinearSet.biUnion · cited by 5IsSemilinearSet.biUnionIsSemilinearSet.iUnion · cited by 1IsSemilinearSet.iUnionSet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidSet.Finite · cited by 1814Set.FiniteSet.sUnion · cited by 392Set.sUnionIsSemilinearSet · cited by 44IsSemilinearSetSet.Finite.induction_on · cited by 39Finite.induction_onSet.sUnion_empty · cited by 17Set.sUnion_emptySet.sUnion_insert · cited by 11Set.sUnion_insertIsSemilinearSet.union · cited by 3IsSemilinearSet.unionIsSemilinearSet.sUnionCITED BYCITES

Cites9

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.