Module: Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic

Goal state before:
pp: case e_a
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ ∑ i ∈ h₁s.toFinset, (↑(((toClosedBall r) D₁) i) + ↑(((toClosedBall r) D₂) i)) * log (r * ‖i‖⁻¹) =
    ∑ i ∈ h₁s.toFinset, ↑(((toClosedBall r) D₁) i) * log (r * ‖i‖⁻¹) +
      ∑ i ∈ h₁s.toFinset, ↑(((toClosedBall r) D₂) i) * log (r * ‖i‖⁻¹)

pp: case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ ↑(((toClosedBall r) D₂) z) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset

pp: case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ ↑(((toClosedBall r) D₁) z) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset

pp: case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ (↑(((toClosedBall r) D₁) z) + ↑(((toClosedBall r) D₂) z)) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset

Tactic:
]

Goal state after:
case e_a
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ ∑ i ∈ h₁s.toFinset, (↑(((toClosedBall r) D₁) i) + ↑(((toClosedBall r) D₂) i)) * log (r * ‖i‖⁻¹) =
    ∑ i ∈ h₁s.toFinset, ↑(((toClosedBall r) D₁) i) * log (r * ‖i‖⁻¹) +
      ∑ i ∈ h₁s.toFinset, ↑(((toClosedBall r) D₂) i) * log (r * ‖i‖⁻¹)

case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ ↑(((toClosedBall r) D₂) z) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset

case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ ↑(((toClosedBall r) D₁) z) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset

case e_a.h
E✝ : Type u_1
inst✝² : NormedAddCommGroup E✝
E : Type u_2
inst✝¹ : NormedAddCommGroup E
inst✝ : ProperSpace E
D₁ D₂ : locallyFinsupp E ℤ
r : ℝ
this : ∀ {A B C D : ℝ}, A + B + (C + D) = A + C + (B + D)
h₁s : (((toClosedBall r) D₁).support ∪ ((toClosedBall r) D₂).support).Finite
⊢ (Function.support fun z ↦ (↑(((toClosedBall r) D₁) z) + ↑(((toClosedBall r) D₂) z)) * log (r * ‖z‖⁻¹)) ⊆ ↑h₁s.toFinset