inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two

English

Negating the second vector flips the sign of the oangle: (o.oangle x (−y)).sign = −(o.oangle x y).sign.

Русский

Отрицание второго вектора меняет знак oangle: (o.oangle x (−y)).sign = −(o.oangle x y).sign.

LaTeX

$$$ (o.oangle x (-y)).sign = -(o.oangle x y).sign $$$

Lean4

/-- If the oriented angle between two vectors is `-π / 2`, the inner product of those vectors
(reversed) is zero. -/
theorem inner_rev_eq_zero_of_oangle_eq_neg_pi_div_two {x y : V} (h : o.oangle x y = (-π / 2 : ℝ)) : ⟪y, x⟫ = 0 := by
  rw [real_inner_comm, o.inner_eq_zero_of_oangle_eq_neg_pi_div_two h]

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