proposition: Theorem partition_intersection l m k : length k < length (l++m) -> incl (l++m) k -> list_has_dup l \/ list_has_dup m \/ exists x, In x l /\ In x m.
proof: Proof. intros H1 H2. apply list_has_dup_app_inv, list_has_dup_eq_duplicates. revert H1 H2; apply finite_pigeon_hole. Qed.
imports: Arith Lia List Permutation Relations Undecidability.Shared.Libs.DLW.Utils(utils_tac utils_list)