Module: Mathlib.Analysis.SpecialFunctions.Pow.Complex

Goal state before:
pp: case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : z = 0
⊢ 1 = 1

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : ¬z = 0
⊢ 1 = 0

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : y * z = 0
h✝¹ : y = 0
h✝ : ¬1 = 0
⊢ 1 = cexp (log 1 * z)

pp: case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : z = 0
⊢ 1 = 1

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : ¬z = 0
⊢ 1 = 0

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : y * z = 0
h✝¹ : ¬y = 0
h✝ : ¬0 = 0
⊢ 1 = cexp (log 0 * z)

pp: case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : z = 0
⊢ 0 = 1

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : ¬z = 0
⊢ 0 = 0

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : ¬y * z = 0
h✝¹ : y = 0
h✝ : ¬1 = 0
⊢ 0 = cexp (log 1 * z)

pp: case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : z = 0
⊢ 0 = 1

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : ¬z = 0
⊢ 0 = 0

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : ¬y * z = 0
h✝¹ : ¬y = 0
h✝ : ¬0 = 0
⊢ 0 = cexp (log 0 * z)

pp: case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝² : ¬x = 0
h✝¹ : cexp (log x * y) = 0
h✝ : z = 0
⊢ cexp (log x * (y * z)) = 1

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝² : ¬x = 0
h✝¹ : cexp (log x * y) = 0
h✝ : ¬z = 0
⊢ cexp (log x * (y * z)) = 0

pp: case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝¹ : ¬x = 0
h✝ : ¬cexp (log x * y) = 0
⊢ cexp (log x * (y * z)) = cexp (log (cexp (log x * y)) * z)

Tactic:
<;>

Goal state after:
case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : z = 0
⊢ 1 = 1

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : ¬z = 0
⊢ 1 = 0

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : y * z = 0
h✝¹ : y = 0
h✝ : ¬1 = 0
⊢ 1 = cexp (log 1 * z)

case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : z = 0
⊢ 1 = 1

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : ¬z = 0
⊢ 1 = 0

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : y * z = 0
h✝¹ : ¬y = 0
h✝ : ¬0 = 0
⊢ 1 = cexp (log 0 * z)

case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : z = 0
⊢ 0 = 1

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : y = 0
h✝¹ : 1 = 0
h✝ : ¬z = 0
⊢ 0 = 0

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : ¬y * z = 0
h✝¹ : y = 0
h✝ : ¬1 = 0
⊢ 0 = cexp (log 1 * z)

case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : z = 0
⊢ 0 = 1

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝⁴ : x = 0
h✝³ : ¬y * z = 0
h✝² : ¬y = 0
h✝¹ : 0 = 0
h✝ : ¬z = 0
⊢ 0 = 0

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝³ : x = 0
h✝² : ¬y * z = 0
h✝¹ : ¬y = 0
h✝ : ¬0 = 0
⊢ 0 = cexp (log 0 * z)

case pos
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝² : ¬x = 0
h✝¹ : cexp (log x * y) = 0
h✝ : z = 0
⊢ cexp (log x * (y * z)) = 1

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝² : ¬x = 0
h✝¹ : cexp (log x * y) = 0
h✝ : ¬z = 0
⊢ cexp (log x * (y * z)) = 0

case neg
x y z : ℂ
h₁ : -π < (log x * y).im
h₂ : (log x * y).im ≤ π
h✝¹ : ¬x = 0
h✝ : ¬cexp (log x * y) = 0
⊢ cexp (log x * (y * z)) = cexp (log (cexp (log x * y)) * z)