Theorems · Theorem · geometry

Finset.weightedVSubOfPoint_congr

∀ {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) {w₁ w₂ : ι → k},
  (∀ i ∈ s, w₁ i = w₂ i) →
    ∀ {p₁ p₂ : ι → P},
      (∀ i ∈ s, p₁ i = p₂ i) → ∀ (b : P), (s.weightedVSubOfPoint p₁ b) w₁ = (s.weightedVSubOfPoint p₂ b) w₂

weightedVSubOfPoint gives equal results for two families of weights and two families of points that are equal on s.

Defined in

Mathlib.LinearAlgebra.AffineSpace.Combination

Cited by

2 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupModuleAddTorsor