Theorems · Theorem · logic and foundations
isSemilinearSet_iff
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsSemilinearSet s ↔ ∃ S, (∀ t ∈ S, IsLinearSet t) ∧ s = ⋃₀ ↑SAn equivalent expression of IsSemilinearSet in terms of Finset instead of Set.Finite.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 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.
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
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- SetLike.coestatement · cited by 8,199
- Set.sUnionstatement · cited by 392
- IsSemilinearSetstatement · cited by 44
- IsLinearSetstatement · cited by 28
- Set.exists_finite_iff_finsetproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- IsSemilinearSet.definableproof · cited by 1