proposition: Lemma subset_trans : forall s1 s2 s3, subset s1 s2 -> subset s2 s3 -> subset s1 s3.
proof: Proof. unfold subset. intros. specialize (H k); specialize (H0 k). destruct (get k s1), (get k s2) , (get k s3) ; simpl in *; try tauto. eapply OBool.order_trans; eauto. Qed.
imports: Cdcl.PatriciaR Cdcl.KeyInt Cdcl.ReifClasses Cdcl.Lib Bool Setoid ZifyBool ZArith Uint63 Lia List Cdcl.Syntax Cdcl.Clause