Theorem  Rstar_transitive:  (x:A)(y:A)(z:A)(Rstar x y)->(Rstar y z)->(Rstar x z).
Proof [x,y:A]
[z:A]
(unf_Rstar [P:A->A->Prop](P x y)->(Rstar y z)->(Rstar x z)
[h:(P0:A->A->Prop)
((u:A)(P0 u u))
->((u:A)(v:A)(w:A)(R u v)->(P0 v w)->(P0 u w))->(P0 x y)]
(h [a,a0:A](Rstar a0 z)->(Rstar a z) [u:A][H:(Rstar u z)]H
[u,v:A]
[w:A]
[t1:(R u v)]
[t2:(Rstar w z)->(Rstar v z)]
[t3:(Rstar w z)](Rstar_R u v z t1 (t2 t3)))).