theorem
proved
term proof
euler_from_8tick
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formal statement (Lean)
156theorem euler_from_8tick :
157 ∀ θ : ℝ, cexp (I * θ) = Complex.cos θ + I * Complex.sin θ := by
proof body
Term-mode proof.
158 intro θ
159 rw [Complex.exp_mul_I]
160 ring
161
162/-- e^{iπ} + 1 = 0 (Euler's identity)
163
164 Often called "the most beautiful equation."
165 In RS, it says: 4 ticks around the circle returns to -1. -/