In the case of (5), the LF representation of the IHRC is something like (8a), in which the empty pronoun is further divided into pro and a free variable R. pro is a variable of type e bound by the universal quantifier in the matrix clause.
r is free variable of type e → (e → t), to which an assignment function g assigns the value in (8b) as a salient two-place predicate in the context.