Theorems · Theorem · convex and discrete geometry

Convexity.IsStarConvexSet.add

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Convexity.ConvexSpace R M]
  [Convexity.IsModuleConvexSpace R M] {x y : M} {s t : Set M},
  Convexity.IsStarConvexSet R x s → Convexity.IsStarConvexSet R y t → Convexity.IsStarConvexSet R (x + y) (s + t)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

0 results in Mathlib

Foundations

Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleConvexity.ConvexSpaceConvexity.IsModuleConvexSpace