Theorems · Theorem · convex and discrete geometry

Convexity.IsStarConvexSet.prod

∀ {R : Type u_1} {X : Type u_2} {Y : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R X] [inst_4 : Convexity.ConvexSpace R Y] {x : X}
  {s : Set X} {t : Set Y} {y : Y},
  Convexity.IsStarConvexSet R x s → Convexity.IsStarConvexSet R y t → Convexity.IsStarConvexSet R (x, y) (s ×ˢ t)

Defined in

Mathlib.Geometry.Convex.Star

Cited by

2 results in Mathlib

Foundations

Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace