Theorems · Theorem · logic and foundations
IsSemilinearSet.closure
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsSemilinearSet s → IsSemilinearSet ↑(AddSubmonoid.closure s)Semilinear sets are closed under additive closure.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 82 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.
Cites17
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
- SetLike.coestatement and proof · cited by 8,199
- Set.Finiteproof · cited by 1,814
- AddSubmonoidstatement · cited by 1,178
- Set.sUnionproof · cited by 392
- AddSubmonoid.closurestatement and proof · cited by 224
- IsSemilinearSetstatement and proof · cited by 44
- Set.Finite.induction_onproof · cited by 39
- IsLinearSetproof · cited by 28
- Set.sUnion_emptyproof · cited by 17
- Set.sUnion_insertproof · cited by 11
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