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Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.isStarConvexSet

∀ {R : Type u_1} {X : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : Convexity.ConvexSpace R X] {x : X} {s : Set X},
  Convexity.IsConvexSet R s → x ∈ s → Convexity.IsStarConvexSet R x s
Defined in
Mathlib.Geometry.Convex.Star
Cited by
0 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace
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Set · cited by 53352SetSemiring · cited by 13802SemiringPartialOrder · cited by 6410PartialOrderIsStrictOrderedRing · cited by 2490IsStrictOrderedRingConvexity.ConvexSpace · cited by 176Convexity.ConvexSpaceConvexity.IsConvexSet · cited by 35Convexity.IsConvexSetConvexity.IsStarConvexSet · cited by 20Convexity.IsStarConvexSetConvexity.IsConvexSet.convexCombPair_mem · cited by 1IsConvexSet.convexCombPai…IsConvexSet.isStarConvexSetCITED BYCITES

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