Theorems · Theorem · convex and discrete geometry

Convexity.sConvexComb_convexCombPair

∀ {R : Type u_1} {M : Type u_3} [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) (hst : s + t = 1)
  (w w' : Convexity.StdSimplex R M),
  Convexity.sConvexComb (Convexity.convexCombPair s t hs ht hst w w') =
    Convexity.convexCombPair s t hs ht hst (Convexity.sConvexComb w) (Convexity.sConvexComb w')

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

1 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderSemiringIsStrictOrderedRingConvexity.ConvexSpace