θ : Angle
⊢ sin (θ + ↑π) = -sin θ
⊢ Function.Antiperiodic sin ↑π
intro θ
case h
x✝ : ℝ
⊢ sin (↑x✝ + ↑π) = -sin ↑x✝
θ : Angle
⊢ sin (θ + ↑π) = -sin θ
induction θ using Real.Angle.induction_on
no goals
case h
x✝ : ℝ
⊢ sin (↑x✝ + ↑π) = -sin ↑x✝
exact Real.sin_antiperiodic _