Theorems · Theorem · convex and discrete geometry
ConvexIndependent.injective
∀ {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}, ConvexIndependent 𝕜 p → Function.Injective pA convex independent family is injective.
- Defined in
- Mathlib.Analysis.Convex.Independent
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.mem_singletonproof · cited by 183
- Set.image_singletonproof · cited by 174
- convexHullproof · cited by 163
- ConvexIndependentstatement and proof · cited by 15
- convexHull_singletonproof · cited by 7
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