Theorems · Theorem · convex and discrete geometry
ConvexIndependent.mono
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : Module 𝕜 E] {s t : Set E}, ConvexIndependent 𝕜 Subtype.val → s ⊆ t → ConvexIndependent 𝕜 Subtype.valA subset of a convex independent set of points is convex independent as well.
- Defined in
- Mathlib.Analysis.Convex.Independent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 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
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- ConvexIndependentstatement and proof · cited by 15
- Set.embeddingOfSubsetproof · cited by 9
- ConvexIndependent.comp_embeddingproof · cited by 4
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