Theorem: Polynomial.discConv_neg_weight (LeanCamCombi/DiscreteDeriv.lean)

State before:
ι : Type u_1
R : Type u_2
S : Type u_3
inst✝² : CommRing R
inst✝¹ : CommRing S
inst✝ : Algebra S R
w✝ : R →₀ S
P✝ : R[X]
w : R →₀ S
P : R[X]
⊢ ∀ (a : R), 0 • P.comp (X + C a) = 0
Tactic:
simp
State after:
no goals

State before:
ι : Type u_1
R : Type u_2
S : Type u_3
inst✝² : CommRing R
inst✝¹ : CommRing S
inst✝ : Algebra S R
w✝ : R →₀ S
P✝ : R[X]
w : R →₀ S
P : R[X]
⊢ (w.sum fun a b => -b • P.comp (X + C a)) = -discConv w P
Tactic:
simp [discConv]
State after:
no goals