Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_indicator_subset

∀ {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} (w : ι → k) (p : ι → P) (b : P) {s₁ s₂ : Finset ι},
  s₁ ⊆ s₂ → (s₁.weightedVSubOfPoint p b) w = (s₂.weightedVSubOfPoint p b) ((↑s₁).indicator w)

The weighted sum is unaffected by changing the weights to the corresponding indicator function and adding points to the set.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor