Theorems · Theorem · convex and discrete geometry

Prod.fst_iConvexComb

∀ {I : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
  {X : Type u_3} {Y : Type u_4} [inst_3 : Convexity.ConvexSpace R X] [inst_4 : Convexity.ConvexSpace R Y]
  (w : Convexity.StdSimplex R I) (f : I → X × Y),
  (Convexity.iConvexComb w f).1 = Convexity.iConvexComb w fun i => (f i).1

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Prod

Cited by

0 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingConvexity.ConvexSpaceConvexity.ConvexSpace