isBipartiteWith_neighborFinset_disjoint

English

If G.IsBipartiteWith s t and v ∈ s, then neighborFinset v is disjoint from s.

Русский

Если G IsBipartiteWith s t и v ∈ s, то neighborFinset v дизjoint от s.

LaTeX

$$G.IsBipartiteWith s t → v ∈ s → Disjoint (G.neighborFinset v) s$$

Lean4

/-- If `G.IsBipartiteWith s t` and `v ∈ s`, then the neighbor finset of `v` is disjoint to `s`. -/
theorem isBipartiteWith_neighborFinset_disjoint (h : G.IsBipartiteWith s t) (hv : v ∈ s) :
    Disjoint (G.neighborFinset v) s :=
  by
  rw [neighborFinset_def, ← disjoint_coe, Set.coe_toFinset]
  exact isBipartiteWith_neighborSet_disjoint h hv

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