Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_sdiff

∀ {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} (s : Finset ι) [inst_3 : DecidableEq ι] {s₂ : Finset ι},
  s₂ ⊆ s →
    ∀ (w : ι → k) (p : ι → P) (b : P),
      ((s \ s₂).weightedVSubOfPoint p b) w + (s₂.weightedVSubOfPoint p b) w = (s.weightedVSubOfPoint p b) w

A weighted sum may be split into such sums over two subsets.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidableEq