Theorems · Theorem · convex and discrete geometry
Subsingleton.convexIndependent
∀ {𝕜 : Type u_1} {E : Type u_2} {ι : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] [Subsingleton ι] (p : ι → E), ConvexIndependent 𝕜 pA family with at most one point is convex independent.
- Defined in
- Mathlib.Analysis.Convex.Independent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- convexHullproof · cited by 163
- Set.image_nonemptyproof · cited by 29
- ConvexIndependentstatement · cited by 15
- convexHull_nonempty_iffproof · cited by 6
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