center_mem_orthRadius_iff — Mathlib

English

Twice the angle between two multiples of the same vector is zero: 2 oangle (r1 x) (r2 x) = 0.

Русский

Вдвое угол между двумя кратными одной и той же величины равен нулю: 2 oangle (r1 x) (r2 x) = 0.

LaTeX

$$$2 \\cdot o.\\!oangle(r_1 x, r_2 x) = 0$$$

Lean4

@[simp]
theorem center_mem_orthRadius_iff {s : Sphere P} {p : P} : s.center ∈ s.orthRadius p ↔ p = s.center :=
  by
  rw [mem_orthRadius_iff_inner_left, ← neg_vsub_eq_vsub_rev, inner_neg_left]
  simp

Похожие утверждения