Theorems · Definition · convex and discrete geometry

Convexity.ConvexSpace.subtype

{R : Type u_3} →
  {X : Type u_5} →
    [inst : Semiring R] →
      [inst_1 : PartialOrder R] →
        [inst_2 : IsStrictOrderedRing R] →
          [inst_3 : Convexity.ConvexSpace R X] → (s : Set X) → Convexity.IsConvexSet R s → Convexity.ConvexSpace R ↑s

A convex subset of a convex space is a convex space.

Defined in

Mathlib.Geometry.Convex.Set

Cited by

4 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace