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Theorems · Theorem · logic and foundations

IsSemilinearSet.sInter

∀ {M : Type u_1} [inst : AddCommMonoid M] [AddMonoid.FG M] {S : Set (Set M)},
  S.Finite → (∀ s ∈ S, IsSemilinearSet s) → IsSemilinearSet (⋂₀ S)
Defined in
Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic
Cited by
2 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommMonoidAddMonoid.FG
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Around this declaration

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

IsSemilinearSet.biInter · cited by 1IsSemilinearSet.biInterIsSemilinearSet.iInter · cited by 0IsSemilinearSet.iInterSet · cited by 53352SetAddCommMonoid · cited by 12281AddCommMonoidSet.Finite · cited by 1814Set.FiniteSet.sInter · cited by 225Set.sInterIsSemilinearSet · cited by 44IsSemilinearSetSet.Finite.induction_on · cited by 39Finite.induction_onAddMonoid.FG · cited by 31AddMonoid.FGSet.sInter_empty · cited by 16Set.sInter_emptySet.sInter_insert · cited by 8Set.sInter_insertIsSemilinearSet.inter · cited by 2IsSemilinearSet.interIsSemilinearSet.sInterCITED BYCITES

Cites10

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.