circumcenter_reindex — Mathlib

English

For 0-simplex, circumcenter equals its unique point.

Русский

Для 0-сложногоCircumcenter равен единственной вершине.

LaTeX

$$$(s : Simplex ℝ P 0).circumcenter = (s.points 0)$$$

Lean4

/-- Reindexing a simplex along an `Equiv` of index types does not change the circumcenter. -/
@[simp]
theorem circumcenter_reindex {m n : ℕ} (s : Simplex ℝ P m) (e : Fin (m + 1) ≃ Fin (n + 1)) :
    (s.reindex e).circumcenter = s.circumcenter := by simp_rw [circumcenter, circumsphere_reindex]

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