proposition: Theorem clauses_merge_in: forall p cs1 cs2, In p (clauses_merge cs1 cs2) <-> In p cs1 \/ In p cs2.
proof: Proof. intros p cs1 cs2; unfold clauses_merge; split; intros H. case add_inv with (1 := H); auto. case H; clear H; intros H. apply add_incl_l; auto. apply add_incl_r; auto. Qed.
imports: List UList Permutation Div OrderedList ListOp Lia