Theorems · Theorem · convex and discrete geometry

Convexity.IsConvexSet.convexCombPair_mem

∀ {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} {x y : X},
  Convexity.IsConvexSet R s →
    x ∈ s →
      y ∈ s → ∀ {a b : R} (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1), Convexity.convexCombPair a b ha hb hab x y ∈ s

Defined in

Mathlib.Geometry.Convex.Set

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpace