Theorems · Theorem · geometry

Finset.affineCombination_piSingle

∀ (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] (p : ι → P) {i : ι},
  i ∈ s → (Finset.affineCombination k s p) (Pi.single i 1) = p i

An affine combination with affineCombinationSingleWeights gives the specified point.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

19 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsorDecidableEq