13 lines
313 B
Lean4
13 lines
313 B
Lean4
import Mathlib
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open Complex
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/--
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Show that a function whose real part vanishes is constant.
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-/
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theorem testCase {f : ℂ → ℂ} {U : Set ℂ} (h₁ : IsOpen U) (h₂ : IsConnected U)
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(h₃ : AnalyticOnNhd ℂ f U) (h₄ : ∀ x ∈ U, (f x).re = 0) :
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∃ c : ℝ, ∀ x ∈ U, f x = c*I := by
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sorry
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