Theorems · Theorem · convex and discrete geometry
convex_list_sum
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] {l : List (Set E)}, (∀ i ∈ l, Convex 𝕜 i) → Convex 𝕜 l.sum- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- Convexstatement and proof · cited by 551
- Set.addstatement · cited by 338
- Set.zerostatement · cited by 87
- convexAddSubmonoidproof · cited by 5
- AddSubmonoid.list_sum_memproof · cited by 2
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