proposition: Theorem clause_insert_in: forall p c cs, In p (clause_insert c cs) <-> p = (length c, c) \/ In p cs.
proof: Proof. intros c cs; unfold clause_insert; split; intros H. case ocons_inv with (1 := H); auto. case H; clear H; intros H; subst. apply ocons_in; auto. apply ocons_incl; auto. Qed.
imports: List UList Permutation Div OrderedList ListOp Lia