Theorems · Definition · convex and discrete geometry
convexAddSubmonoid
(𝕜 : Type u_1) →
(E : Type u_2) →
[inst : Semiring 𝕜] → [PartialOrder 𝕜] → [inst_2 : AddCommMonoid E] → [Module 𝕜 E] → AddSubmonoid (Set E)The convex sets form an additive submonoid under pointwise addition.
- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- AddSubmonoidstatement · cited by 1,178
- Convexproof · cited by 551
- Set.addZeroClassstatement · cited by 7
- Convex.addproof · cited by 6
- convex_zeroproof · cited by 0
Cited by5
Results whose statement or proof uses this declaration.
- convex_sumproof · cited by 1
- convex_list_sumproof · cited by 0
- convex_multiset_sumproof · cited by 0
- mem_convexAddSubmonoidstatement · cited by 0
- coe_convexAddSubmonoidstatement · cited by 0