Fixpoint Cond0 (A:Type) (Interp:A->R) (l:list A) : Prop :=
  match l with
  | List.nil => True
  | a::l => Interp a == 0 /\ Cond0 A Interp l
  end.

Lemma check_correct : forall l lpe qe certif, check lpe qe certif = true -> Cond0 PEZ (PEevalR l) lpe -> PEevalR l qe == 0.