sin_eq_real_sin_iff_eq_or_add_eq_pi

English

For a Real.Angle θ and a Real ψ, sin θ = Real.sin ψ iff θ = ψ or θ + ψ = π.

Русский

Для Real.Angle θ и Real ψ, sin θ = Real.sin ψ эквивалентно θ = ψ или θ + ψ = π.

LaTeX

$$$\sin \theta = \mathrm{Real}.\sin \psi \iff \theta = \psi \lor \theta + \psi = \pi$$$

Lean4

theorem sin_eq_real_sin_iff_eq_or_add_eq_pi {θ : Angle} {ψ : ℝ} : sin θ = Real.sin ψ ↔ θ = ψ ∨ θ + ψ = π :=
  by
  induction θ using Real.Angle.induction_on
  exact sin_eq_iff_coe_eq_or_add_eq_pi

Похожие утверждения