Theorems · Theorem · logic and foundations
isLinearSet_iff
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsLinearSet s ↔ ∃ a t, s = a +ᵥ ↑(AddSubmonoid.closure ↑t)An equivalent expression of IsLinearSet in terms of Finset instead of Set.Finite.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 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.
Cites11
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 and proof · cited by 8,199
- HVAdd.hVAddstatement and proof · cited by 1,820
- Set.Finiteproof · cited by 1,814
- AddSubmonoidstatement · cited by 1,178
- Set.vaddSetstatement · cited by 403
- AddSubmonoid.closurestatement and proof · cited by 224
- Set.Finite.coe_toFinsetproof · cited by 124
- IsLinearSetstatement · cited by 28
Cited by3
Results whose statement or proof uses this declaration.
- IsLinearSet.definableproof · cited by 1
- isLinearSet_iff_exists_fg_eq_vaddproof · cited by 1
- IsLinearSet.isProperSemilinearSetproof · cited by 1