Theorem: WI_sum_le (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✝ : _root_.RCLike 𝕜
f : ℕ → ℝ
g₁ g₂ : ℝ → ℝ
hf : 0 ≤ f
hg : g₁ ≤ g₂
hx : 0 < x
hg₁ : HasCompactSupport g₁
hg₂ : HasCompactSupport g₂
⊢ (∑' (n : ℕ), f n * g₁ (↑n / x)) / x ≤ (∑' (n : ℕ), f n * g₂ (↑n / x)) / x
Tactic:
apply div_le_div_of_nonneg_right ?_ hx.le
State after:
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✝ : _root_.RCLike 𝕜
f : ℕ → ℝ
g₁ g₂ : ℝ → ℝ
hf : 0 ≤ f
hg : g₁ ≤ g₂
hx : 0 < x
hg₁ : HasCompactSupport g₁
hg₂ : HasCompactSupport g₂
⊢ ∑' (n : ℕ), f n * g₁ (↑n / x) ≤ ∑' (n : ℕ), f n * g₂ (↑n / x)

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✝ : _root_.RCLike 𝕜
f : ℕ → ℝ
g₁ g₂ : ℝ → ℝ
hf : 0 ≤ f
hg : g₁ ≤ g₂
hx : 0 < x
hg₁ : HasCompactSupport g₁
hg₂ : HasCompactSupport g₂
⊢ ∑' (n : ℕ), f n * g₁ (↑n / x) ≤ ∑' (n : ℕ), f n * g₂ (↑n / x)
Tactic:
exact tsum_le_tsum (fun n => mul_le_mul_of_nonneg_left (hg _) (hf _)) (WI_summable hg₁ hx) (WI_summable hg₂ hx)
State after:
no goals