proposition: Theorem clause_merge_in: forall l c1 c2, In l (clause_merge c1 c2) <-> In l c1 \/ In l c2.
proof: Proof. unfold clause_merge; intros l c1 c2; split; intros H. apply merge_inv with (1 := H); auto. case H; intros H1. apply merge_incl_l; auto. apply merge_incl_r; auto. exact lit_test_exact. Qed.
imports: List UList Permutation Div OrderedList ListOp Lia