no goals
k : Type u_3
V : Type u_1
P : Type u_4
inst✝² : Ring k
inst✝¹ : AddCommGroup V
inst✝ : Module k V
S : AffineSpace V P
ι : Type u_2
s : Finset ι
ι₂ : Type ?u.94059
s₂ : Finset ι₂
w : ι → k
p₁ p₂ : ι → P
b : P
⊢ ∑ i in s, w i • (p₁ i -ᵥ p₂ i) = ↑(weightedVSubOfPoint s p₁ b) w - ↑(weightedVSubOfPoint s p₂ b) w
simp_rw [weightedVSubOfPoint_apply, ← sum_sub_distrib, ← smul_sub, vsub_sub_vsub_cancel_right]