Theorems · Theorem · convex and discrete geometry

Convexity.convexCombPair_eq_sum

∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : PartialOrder R] [inst_2 : IsStrictOrderedRing R]
  [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Convexity.ConvexSpace R M]
  [Convexity.IsModuleConvexSpace R M] (a b : R) (ha : 0 ≤ a) (hb : 0 ≤ b) (hab : a + b = 1) (x y : M),
  Convexity.convexCombPair a b ha hb hab x y = a • x + b • y

convexCombPair in a module can be expressed as a sum.

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleConvexity.ConvexSpaceConvexity.IsModuleConvexSpace