Theorems · Theorem · convex and discrete geometry

Convexity.iConvexComb_convexCombPair_comm

∀ {R : Type u_9} {M : Type u_10} {I : Type u_11} [inst : PartialOrder R] [inst_1 : CommSemiring R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : Convexity.ConvexSpace R M] {s t : R} (hs : 0 ≤ s) (ht : 0 ≤ t)
  (h : s + t = 1) (f : Convexity.StdSimplex R I) (e₁ e₂ : I → M),
  (Convexity.iConvexComb f fun x => Convexity.convexCombPair s t hs ht h (e₁ x) (e₂ x)) =
    Convexity.convexCombPair s t hs ht h (Convexity.iConvexComb f e₁) (Convexity.iConvexComb f e₂)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Defs

Cited by

2 results in Mathlib

Foundations

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

Assumes

PartialOrderCommSemiringIsStrictOrderedRingConvexity.ConvexSpace