symm — Mathlib

English

An affine subspace is in commonExtTangents(s1,s2) iff it is in commonTangents(s1,s2) and no p ∈ as lies weakly between centers.

Русский

Аффинное подпредпосылка принадлежит commonExtTangents, если она принадлежит commonTangents и нет точки между центрами.

LaTeX

$$$ as \\in s_1.commonExtTangents s_2 \\iff as \\in s_1.commonTangents s_2 ∧ \\forall p \\in as, \\neg Sbtw \\ s_1.center p s_2.center $$$

Lean4

theorem symm {s₁ s₂ : Sphere P} (h : s₁.IsExtTangent s₂) : s₂.IsExtTangent s₁ :=
  by
  rcases h with ⟨p, hp⟩
  exact ⟨p, hp.symm⟩

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