Theorems · Theorem · convex and discrete geometry
Function.Injective.convexIndependent_iff_set
∀ {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] {p : ι → E}, Function.Injective p → (ConvexIndependent 𝕜 Subtype.val ↔ ConvexIndependent 𝕜 p)The range of an injective indexed family of points is convex independent iff that family is.
- Defined in
- Mathlib.Analysis.Convex.Independent
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- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setstatement · 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.rangestatement · cited by 4,705
- Set.mem_range_selfproof · cited by 328
- Subtype.mk_eq_mkproof · cited by 33
- ConvexIndependentstatement and proof · cited by 15
- ConvexIndependent.comp_embeddingproof · cited by 4
- ConvexIndependent.rangeproof · cited by 1
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