dedup_append — Mathlib

English

If xs and ys are disjoint, then dedup(xs ++ ys) = dedup(xs) ++ dedup(ys).

Русский

Если xs и ys дисjoint, то dedup(xs ++ ys) = dedup(xs) ++ dedup(ys).

LaTeX

$$$xs \\ Disjoint\\ ys \\Rightarrow \\mathrm{dedup}(xs ++ ys) = \\mathrm{dedup}(xs) ++ \\mathrm{dedup}(ys)$$$

Lean4

theorem dedup_append {xs ys : List α} (h : Disjoint xs ys) : dedup (xs ++ ys) = dedup xs ++ dedup ys :=
  by
  rw [List.dedup_append, Disjoint.union_eq]
  intro a hx hy
  exact h hx (mem_dedup.mp hy)

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