Theorems · Theorem · logic and foundations
IsSemilinearSet.compl
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M} [AddMonoid.FG M], IsSemilinearSet s → IsSemilinearSet sᶜSemilinear sets in a finitely generated monoid are closed under complement.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddMonoid.FG
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
- Compl.complstatement · cited by 2,925
- IsSemilinearSetstatement and proof · cited by 44
- Set.compl_eq_univ_sdiffproof · cited by 43
- AddMonoid.FGstatement and proof · cited by 31
- IsSemilinearSet.sdiffproof · cited by 1
- IsSemilinearSet.univproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- FirstOrder.Language.presburger.isSemilinearSet_boundedFormula_realizeproof · cited by 1