Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair_iConvexComb_right

∀ {R : Type u_1} {M : Type u_3} {J : Type u_7} [inst : PartialOrder R] [inst_1 : Semiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] {s t : R} (hs : 0 ≤ s) (ht : 0 ≤ t)
  (h : s + t = 1) (m : M) (g : Convexity.StdSimplex R J) (e : J → M),
  Convexity.convexCombPair s t hs ht h m (Convexity.iConvexComb g e) =
    Convexity.sConvexComb
      (Convexity.convexCombPair s t hs ht h (Convexity.StdSimplex.single m) (Convexity.StdSimplex.map e g))

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace