Theorem: Finset.sum_shift_front' (PrimeNumberTheoremAnd/Wiener.lean)

State before:
n : ℕ
A a b c d u✝ x y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝¹ : _root_.RCLike 𝕜
E : Type u_1
inst✝ : Ring E
u : ℕ → E
⊢ shift (cumsum u) = (fun x => u 0) + cumsum (shift u)
Tactic:
ext n
State after:
case h
n✝ : ℕ
A a b c d u✝ x y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝¹ : _root_.RCLike 𝕜
E : Type u_1
inst✝ : Ring E
u : ℕ → E
n : ℕ
⊢ shift (cumsum u) n = ((fun x => u 0) + cumsum (shift u)) n

State before:
case h
n✝ : ℕ
A a b c d u✝ x y t σ' : ℝ
ψ Ψ : ℝ → ℂ
F G : ℂ → ℂ
f : ℕ → ℂ
𝕜 : Type
inst✝¹ : _root_.RCLike 𝕜
E : Type u_1
inst✝ : Ring E
u : ℕ → E
n : ℕ
⊢ shift (cumsum u) n = ((fun x => u 0) + cumsum (shift u)) n
Tactic:
apply Finset.sum_shift_front
State after:
no goals