[TYPES] \lambda 2 a subset of System F?

[Edsko de Vries]

Hi,

(Sorry to be asking these basic questions) In his description of the
lambda cube, Barendregt mentions that his system "\lambda 2" (with (*,*)
and ([], *)) is a subset of System F. In what sense is it a subset? It
seems to me that there is a rather direct mapping from the System F
typing rules (as described in "System F of variable types: 15 years
later", for example) to the specialization of Barendregt's Forall and
Abs rules to (*,*) and ([], *). Are there terms that can be typed in
System F that cannot be typed in \lambda 2? (I don't have a copy of
Girard's original thesis and so have to rely on later definitions,
unfortunately.) 

Thanks,

Edsko