Definition demorgan_or (P:list bool -> Prop) l l' := ~ (P l /\ P l') -> ~ P l \/ ~ P l'.
Definition demorgan_inductively_barred_at P :=
forall n l, demorgan_or (inductively_barred_at P n) (true::l) (false::l).

Lemma is_path_from_imp_inductively_barred_at : forall P n l,
is_path_from P n l -> inductively_barred_at P n l -> False.