Theorems · Theorem · geometry

Finset.weightedVSub_filter_of_ne

∀ {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) {pred : ι → Prop}
  [inst_3 : DecidablePred pred],
  (∀ i ∈ s, w i ≠ 0 → pred i) → ({x ∈ s | pred x}.weightedVSub p) w = (s.weightedVSub p) w

A weighted sum over {x ∈ s | pred x} equals one over s if all the weights at indices in s not satisfying pred are zero.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

1 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidablePred