angle_comm — Mathlib

English

Let x and y be vectors in a real inner product space. Then the angle between x and y equals the angle between y and x.

Русский

Пусть x и y — векторы в вещественном пространстве с скалярным произведением. Угол между x и y равен углу between y и x.

LaTeX

$$$\\\\angle x y = \\\\angle y x$$$

Lean4

/-- The angle between two vectors does not depend on their order. -/
theorem angle_comm (x y : V) : angle x y = angle y x :=
  by
  unfold angle
  rw [real_inner_comm, mul_comm]

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