dist_lt_dist_add_dist_iff — Mathlib

English

If dist x y and dist x z are both equal to half of dist x z, then y is the midpoint of x and z.

Русский

Если расстояния dist(x,y) и dist(x,z) равны половине dist(x,z), то y — середина отрезка xz.

LaTeX

$$eq_midpoint_of_dist_eq_half$$

Lean4

/-- The strict triangle inequality. -/
theorem dist_lt_dist_add_dist_iff {a b c : P} : dist a c < dist a b + dist b c ↔ ¬Wbtw ℝ a b c := by
  rw [← ne_iff_lt_iff_le.mpr (dist_triangle _ _ _), not_iff_not, eq_comm, dist_add_dist_eq_iff]

Похожие утверждения