Class Exists_NE :=
exists_NE : Zeven beta = false \/ forall e,
((fexp e < e)%Z -> (fexp (e + 1) < e)%Z) /\ ((e <= fexp e)%Z -> fexp (fexp e + 1) = fexp e).
Context { exists_NE_ : Exists_NE }.

Theorem DN_UP_parity_generic_pos :
DN_UP_parity_pos_prop.