have ⟨m, _⟩ := Set.Nonempty.iff_exists_mem.mp h.nonempty
W : Set (Nat⋆)
h : TreeDomain W
⊢ ∃ m, Set.image Word.prefixes m ∧ m Word.ε
W : Set (Nat⋆)
h : TreeDomain W
m : Nat⋆
h✝ : m ∈ W
⊢ ∃ m, Set.image Word.prefixes m ∧ m Word.ε