Theorems · Theorem · functional analysis
absConvexHull_add_subset
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] {s t : Set E}, (absConvexHull 𝕜) (s + t) ⊆ (absConvexHull 𝕜) s + (absConvexHull 𝕜) t- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- PartialOrderstatement and proof · cited by 6,410
- ClosureOperatorstatement · cited by 371
- Set.addstatement · cited by 338
- absConvexHullstatement · cited by 29
- Set.add_subset_addproof · cited by 18
- subset_absConvexHullproof · cited by 7
- Convex.addproof · cited by 6
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