Theorem: smooth_urysohn (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
a b c d : ℝ
h1 : a < b
h3 : c < d
⊢ ∃ Ψ, ContDiff ℝ ⊤ Ψ ∧ HasCompactSupport Ψ ∧ (Icc b c).indicator 1 ≤ Ψ ∧ Ψ ≤ (Ioo a d).indicator 1
Tactic:
obtain ⟨ψ, l1, l2, l3, l4, -⟩ := smooth_urysohn_support_Ioo h1 h3
State after:
case intro.intro.intro.intro.intro
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
a b c d : ℝ
h1 : a < b
h3 : c < d
ψ : ℝ → ℝ
l1 : ContDiff ℝ ⊤ ψ
l2 : HasCompactSupport ψ
l3 : (Icc b c).indicator 1 ≤ ψ
l4 : ψ ≤ (Ioo a d).indicator 1
⊢ ∃ Ψ, ContDiff ℝ ⊤ Ψ ∧ HasCompactSupport Ψ ∧ (Icc b c).indicator 1 ≤ Ψ ∧ Ψ ≤ (Ioo a d).indicator 1

State before:
case intro.intro.intro.intro.intro
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
a b c d : ℝ
h1 : a < b
h3 : c < d
ψ : ℝ → ℝ
l1 : ContDiff ℝ ⊤ ψ
l2 : HasCompactSupport ψ
l3 : (Icc b c).indicator 1 ≤ ψ
l4 : ψ ≤ (Ioo a d).indicator 1
⊢ ∃ Ψ, ContDiff ℝ ⊤ Ψ ∧ HasCompactSupport Ψ ∧ (Icc b c).indicator 1 ≤ Ψ ∧ Ψ ≤ (Ioo a d).indicator 1
Tactic:
refine ⟨ψ, l1, l2, l3, l4⟩
State after:
no goals