disjoint_support_of_append — Mathlib

English

If p.append q is a path and q is nonempty, then p.support is disjoint from q.tail.support.

Русский

Если p.append q — путь и q непуст, то поддержка p не пересекается с поддержкой хвоста q.

LaTeX

$$$ (p.append q).IsPath \Rightarrow q.Nordic? NotNil \Rightarrow p.support.Disjoint q.tail.support $$$

Lean4

theorem disjoint_support_of_append {p : G.Walk u v} {q : G.Walk v w} (hpq : (p.append q).IsPath) (hq : ¬q.Nil) :
    p.support.Disjoint q.tail.support := by
  have hpq' := hpq.support_nodup
  rw [support_append] at hpq'
  rw [support_tail_of_not_nil q hq]
  exact List.disjoint_of_nodup_append hpq'

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