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[Zhong Shao <shao AT cs.yale.edu>]

Hi, given the following induction definition: 

   Inductive R (A : Set) : Type := 
        Rep : A -> R(A).

assume that Set is a predicative universe (as in Coq 8.0),

Can I write a function F with the following type: 

            (forall A B : Set) A -> R(A -> B) -> R(B)

The naive way is to write it as: 

  Definition F (A B : Set) (x : A) (y : R(A->B)) : R(B) := 
     match y with 
       Rep y0 => Rep (y0 x)
     end.

which of course does not work since y0 does not has type A->B.

Thanks a lot,

-Zhong Shao
(shao-zhong AT cs.yale.edu)