rotation_symm — Mathlib

English

The inverse of rotation by θ is the rotation by −θ: (o.rotation(θ)).symm = o.rotation(−θ).

Русский

Обратный поворот на θ равен повороту на −θ: (o.rotation(θ)).symm = o.rotation(−θ).

LaTeX

$$$ (o.rotation(\theta)).symm = o.rotation(-\theta) $$$

Lean4

/-- The inverse of `rotation` is rotation by the negation of the angle. -/
@[simp]
theorem rotation_symm (θ : Real.Angle) : (o.rotation θ).symm = o.rotation (-θ) := by ext;
  simp [o.rotation_apply, o.rotation_symm_apply, sub_eq_add_neg]

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