Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_insert

∀ {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] (w : ι → k) (p : ι → P) (i : ι),
  ((insert i s).weightedVSubOfPoint p (p i)) w = (s.weightedVSubOfPoint p (p i)) w

The weighted sum is unaffected by adding the base point, whether or not present, to the set of points.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidableEq