proposition: Lemma check_correct : forall l lpe qe certif, check lpe qe certif = true -> Cond0 PEZ (PEevalR l) lpe -> PEevalR l qe == 0.
proof: Proof. unfold check;intros l lpe qe (lla, lq) H2 H1. apply PolZeq_correct with (l:=l) in H2. rewrite norm_correct, H2. apply mult_l_correct. apply compute_list_correct. clear H2 lq lla qe;induction lpe;simpl;trivial. simpl in H1;destruct H1. rewrite <- norm_correct;auto. Qed.
imports: List Setoid BinPos BinList Znumtheory Morphisms Setoid Bool Algebra_syntax Ncring Ncring_initial Ncring_tac Integral_domain ZArith Lia