Theorems · Theorem · logic and foundations
isLinearSet_iff_exists_fg_eq_vadd
∀ {M : Type u_1} [inst : AddCommMonoid M] {s : Set M}, IsLinearSet s ↔ ∃ a P, P.FG ∧ s = a +ᵥ ↑P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 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
- Finsetproof · 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
- AddSubmonoidstatement and proof · cited by 1,178
- Set.vaddSetstatement · cited by 403
- AddSubmonoid.closureproof · cited by 224
- AddSubmonoid.FGstatement and proof · cited by 36
- IsLinearSetstatement · cited by 28
- isLinearSet_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsLinearSet.of_fgproof · cited by 2