  We give a type system in which the universe of types is closed by reflection
into it of the logical relation defined externally by induction on the
structure of types. This contribution is placed in the context of the search
for a natural, syntactic construction of the extensional equality type (Tait
[1995], Altenkirch [1999], Coquand [2011], Licata and Harper [2012], Martin-Lof
[2013]). The system is presented as an extension of lambda-*, the terminal pure
type system in which the universe of all types is a type. The universe
inconsistency is then removed by the usual method of stratification into
levels. We give a set-theoretic model for the stratified system. We conjecture
that Strong Normalization holds as well.
