Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.sInter

∀ {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 (Set X)},
  (∀ s ∈ S, Convexity.IsConvexSet R s) → Convexity.IsConvexSet R (⋂₀ S)

Defined in

Mathlib.Geometry.Convex.Set

Cited by

3 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace