simp only [← mem_direct_succ_list_iff]
Node : Type
inst✝ : DecidableEq Node
g : Graph Node
⊢ ∀ (xs : List Node) (y : Node),
    y ∈ (List.map (fun x => direct_succ_list g x) xs).join ↔ ∃ x ∈ xs, ∃ ys, y ∈ ys ∧ (x, ys) ∈ g
Node : Type
inst✝ : DecidableEq Node
g : Graph Node
⊢ ∀ (xs : List Node) (y : Node),
    y ∈ (List.map (fun x => direct_succ_list g x) xs).join ↔ ∃ x ∈ xs, y ∈ direct_succ_list g x