Theorem: comp_exp_support2 (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
Ψ : ℝ → ℂ
hsupp : HasCompactSupport Ψ
⊢ ∀ᶠ (x : ℝ) in atTop, (Ψ ∘ rexp) x = 0
Tactic:
simp only [hasCompactSupport_iff_eventuallyEq, coclosedCompact_eq_cocompact, cocompact_eq_atBot_atTop] at hsupp
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
Ψ : ℝ → ℂ
hsupp : Ψ =ᶠ[atBot ⊔ atTop] 0
⊢ ∀ᶠ (x : ℝ) in atTop, (Ψ ∘ rexp) x = 0

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
Ψ : ℝ → ℂ
hsupp : Ψ =ᶠ[atBot ⊔ atTop] 0
⊢ ∀ᶠ (x : ℝ) in atTop, (Ψ ∘ rexp) x = 0
Tactic:
exact Real.tendsto_exp_atTop hsupp.2
State after:
no goals