mem_commonTangents_iff — Mathlib

English

An affine subspace is in the common tangents of s1 and s2 iff it lies in both tangent sets: as ∈ s1.commonTangents s2 ↔ as ∈ s1.tangentSet ∧ as ∈ s2.tangentSet.

Русский

Аффинное подпредпосылка пространства принадлежит общим касательным сферам, если и только если она принадлежит обоим касательным множествам: as ∈ s1.commonTangents s2 ⇔ as ∈ s1.tangentSet ∧ as ∈ s2.tangentSet.

LaTeX

$$$ as \\in s_1.commonTangents s_2 \\iff as \\in s_1.tangentSet \\land as \\in s_2.tangentSet $$$

Lean4

theorem mem_commonTangents_iff {as : AffineSubspace ℝ P} {s₁ s₂ : Sphere P} :
    as ∈ s₁.commonTangents s₂ ↔ as ∈ s₁.tangentSet ∧ as ∈ s₂.tangentSet :=
  Iff.rfl

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