Theorems · Theorem · convex and discrete geometry
convex_openSegment
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : CommSemiring 𝕜] [inst_1 : PartialOrder 𝕜] [IsStrictOrderedRing 𝕜]
[inst_3 : AddCommGroup E] [inst_4 : Module 𝕜 E] (a b : E), Convex 𝕜 (openSegment 𝕜 a b)- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- CommSemiringstatement and proof · cited by 10,911
- PartialOrderstatement and proof · cited by 6,410
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- IsStrictOrderedRingstatement and proof · cited by 2,490
- zero_addproof · cited by 2,366
- Convexstatement · cited by 551
- mul_addproof · cited by 413
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