Theorem: Polynomial.eval_discForwardDiff (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✝ P : R[X]
x : R
⊢ eval x P.discForwardDiff = eval (x + 1) P - eval x P
Tactic:
simp_rw [discForwardDiff, discConv_sub_weight, discConv_single]
State after:
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✝ P : R[X]
x : R
⊢ eval x (1 • P.comp (X + C 1) - 1 • P.comp (X + C 0)) = eval (x + 1) P - eval x P

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✝ P : R[X]
x : R
⊢ eval x (1 • P.comp (X + C 1) - 1 • P.comp (X + C 0)) = eval (x + 1) P - eval x P
Tactic:
simp
State after:
no goals