Theorems · Theorem · geometry

Finset.affineCombination_of_eq_one_of_eq_zero

∀ {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) {i : ι},
  i ∈ s → w i = 1 → (∀ i2 ∈ s, i2 ≠ i → w i2 = 0) → (Finset.affineCombination k s p) w = p i

An affineCombination equals a point if that point is in the set and has weight 1 and the other points in the set have weight 0.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

8 results in Mathlib

Foundations

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

Assumes

RingAddCommGroupModuleAddTorsor