Theorems · Definition · convex and discrete geometry

affineSegment

(R : Type u_1) →
  {V : Type u_2} →
    {P : Type u_4} →
      [inst : Ring R] → [PartialOrder R] → [inst_2 : AddCommGroup V] → [Module R V] → [AddTorsor V P] → P → P → Set P

The segment of points weakly between x and y. When convexity is refactored to support abstract affine combination spaces, this will no longer need to be a separate definition from segment. However, lemmas involving +ᵥ or -ᵥ will still be relevant after such a refactoring, as distinct from versions involving + or - in a module.

Defined in

Mathlib.Analysis.Convex.Between

Cited by

22 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Quot.sound

Assumes

RingPartialOrderAddCommGroupModuleAddTorsor