proposition: Lemma beval_split_clause : forall env cl1 n1 p1, Elim.split_clause cl1 = (n1, p1) -> beval_clause env cl1 = beval_clause env(n1 ++ p1).
proof: Proof. induction cl1. - simpl. intros. inv H. reflexivity. - intros. simpl in H. destruct a. inv H. simpl. reflexivity. destruct (Elim.split_clause cl1) as (ln2,lp2) eqn:SC. inv H. simpl. erewrite IHcl1; eauto. Qed.
imports: ZArith List Bool Lia Morphisms Cdcl.Syntax Cdcl.Lib Cdcl.Lit Cdcl.Clause