Theorems · Theorem · geometry

Finset.weightedVSub_const_smul

∀ {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) (w : ι → k) (p : ι → P) (c : k),
  (s.weightedVSub p) (c • w) = c • (s.weightedVSub p) w

A constant multiplier of the weights in weightedVSub_of may be moved outside the sum.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

3 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor