Theorems · Theorem · convex and discrete geometry

Convexity.IsAffineMap.map_sum_weights

∀ {R : Type u_2} {M : Type u_3} {N : Type u_4} {I : Type u_5} [inst : Semiring R] [inst_1 : PartialOrder R]
  [inst_2 : IsStrictOrderedRing R] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : AddCommMonoid N]
  [inst_6 : Module R N] {f : M → N} [inst_7 : Convexity.ConvexSpace R M] [Convexity.IsModuleConvexSpace R M]
  [inst_9 : Convexity.ConvexSpace R N] [Convexity.IsModuleConvexSpace R N],
  Convexity.IsAffineMap R f →
    ∀ (w : Convexity.StdSimplex R I) (g : I → M),
      f (w.weights.sum fun i r => r • g i) = w.weights.sum fun i r => r • f (g i)

Defined in

Mathlib.Geometry.Convex.ConvexSpace.Module

Cited by

2 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderIsStrictOrderedRingAddCommMonoidModuleAddCommMonoidModuleConvexity.ConvexSpaceConvexity.IsModuleConvexSpaceConvexity.ConvexSpaceConvexity.IsModuleConvexSpace