Theorems · Theorem · geometry

AffineIndependent.indicator_eq_of_affineCombination_eq

∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
  [inst_3 : AddTorsor V P] {ι : Type u_4} {p : ι → P},
  AffineIndependent k p →
    ∀ (s₁ s₂ : Finset ι) (w₁ w₂ : ι → k),
      ∑ i ∈ s₁, w₁ i = 1 →
        ∑ i ∈ s₂, w₂ i = 1 →
          (Finset.affineCombination k s₁ p) w₁ = (Finset.affineCombination k s₂ p) w₂ →
            (↑s₁).indicator w₁ = (↑s₂).indicator w₂

Defined in

Mathlib.LinearAlgebra.AffineSpace.Independent

Cited by

3 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor