box_succ_disjUnion — Mathlib

English

The hollow box grows by disjoint union with the inner interval: box(n+1) disjointUnion Icc(-n,n) = Icc(-n.succ, n.succ).

Русский

Полость(box) растёт за счёт расщепления на дисjointUnion внутреннего интервала: box(n+1) disjointUnion Icc(-n,n) = Icc(-n.succ, n.succ).

LaTeX

$$$\mathrm{box}(n+1) \ \hspace{-1pt}\mathbin{\disjointUnion}\ \mathrm{Icc}(-n, n) = \mathrm{Icc}(-n.succ, n.succ)$$$

Lean4

theorem box_succ_disjUnion (n : ℕ) :
    (box (n + 1)).disjUnion (Icc (-n : α) n) (disjoint_box_succ_prod _) = Icc (-n.succ : α) n.succ := by
  rw [disjUnion_eq_union, box_succ_union_prod]

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