Theorems · Theorem · convex and discrete geometry

Convexity.iConvexComb_comm

∀ {R : Type u_9} {M : Type u_10} {I : Type u_11} {J : Type u_12} [inst : PartialOrder R] [inst_1 : CommSemiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] (f : Convexity.StdSimplex R I)
  (g : Convexity.StdSimplex R J) (e : I → J → M),
  (Convexity.iConvexComb f fun i => Convexity.iConvexComb g (e i)) =
    Convexity.iConvexComb g fun j => Convexity.iConvexComb f fun i => e i j

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

1 results in Mathlib

Foundations

Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderCommSemiringIsStrictOrderedRingConvexity.ConvexSpace