log_div_self — Mathlib

English

If x,y ∈ ℂ lie in the strip -π < Im(·) ≤ π and exp x = exp y, then x = y.

Русский

Если x,y ∈ ℂ лежат в полосе -π < Im(·) ≤ π и exp x = exp y, то x = y.

LaTeX

$$$\text{If } -\pi < \operatorname{Im}(x) \le \pi \text{ and } -\pi < \operatorname{Im}(y) \le \pi,\ \exp x = \exp y \Rightarrow x = y.$$$

Lean4

/-- This holds true for all `x : ℂ` because of the junk values `0 / 0 = 0` and `log 0 = 0`. -/
@[simp]
theorem log_div_self (x : ℂ) : log (x / x) = 0 := by simp [log]

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