Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_map

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [S : AddTorsor V P] {ι : Type u_4} {ι₂ : Type u_5} (s₂ : Finset ι₂) (e : ι₂ ↪ ι) (w : ι → k) (p : ι → P) (b : P),
  ((Finset.map e s₂).weightedVSubOfPoint p b) w = (s₂.weightedVSubOfPoint (p ∘ ⇑e) b) (w ∘ ⇑e)

A weighted sum, over the image of an embedding, equals a weighted sum with the same points and weights over the original Finset.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor