Theorems · Theorem · functional analysis
zero_mem_absConvexHull
∀ {𝕜 : Type u_1} {E : Type u_2} {s : Set E} [inst : SeminormedRing 𝕜] [inst_1 : PartialOrder 𝕜]
[inst_2 : AddCommGroup E] [inst_3 : Module 𝕜 E] [Nonempty ↑s], 0 ∈ (absConvexHull 𝕜) s- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- Set.Elemstatement and proof · cited by 7,166
- PartialOrderstatement and proof · cited by 6,410
- SeminormedRingstatement and proof · cited by 446
- ClosureOperatorstatement · cited by 371
- Set.Nonempty.monoproof · cited by 88
- absConvexHullstatement · cited by 29
- subset_absConvexHullproof · cited by 7
- Set.Nonempty.of_subtypeproof · cited by 5
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