Theorems · Theorem · convex and discrete geometry
convex_segment
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
[inst_3 : Module 𝕜 E] [IsOrderedRing 𝕜] (x y : E), Convex 𝕜 (segment 𝕜 x y)- Defined in
- Mathlib.Analysis.Convex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- 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
- zero_addproof · cited by 2,366
- IsOrderedRingstatement and proof · cited by 777
- Convexstatement · cited by 551
- mul_addproof · cited by 413
Cited by5
Results whose statement or proof uses this declaration.
- convexHull_pairproof · cited by 3
- Convex.isLittleO_pow_succproof · cited by 1
- Sion.exists_lt_iInf_of_lt_iInf_of_supproof · cited by 1
- convex_parallelepipedproof · cited by 0
- Real.dimH_segmentproof · cited by 0