define-predicate fails to define predicate for Refine

What version of Racket are you using?

Racket 7.7

What program did you run?

#lang typed/racket
(define-type Rational (U Integer (Pair Rational Non-Zero-Rational)))
(define-type Zero-Rational (U Zero (Pair Zero-Rational Non-Zero-Rational)))
(define-type Non-Zero-Rational (Refine [num : Rational] (! num Zero-Rational)))

(define-predicate rat? Rational)

(: make-rational (case-> [-> Rational Non-Zero-Rational Rational]
                         [-> Rational Rational]))
(define make-rational
  (case-lambda
    [(r) r]
    [(r1 r2)
     (cons r1 r2)]))

(displayln (rat? (make-rational 3 2)))

What should have happened?

#t

If you got an error message, please include it here.

car: contract violation
  expected: pair?
  given: #f
  context...:
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/static-contracts/instantiate.rkt:90:2: loop
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/static-contracts/instantiate.rkt:80:0: compute-defs
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/static-contracts/instantiate.rkt:109:0: compute-constraints
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/private/type-contract.rkt:230:0: get-max-contract-kind
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/private/type-contract.rkt:438:10: for-loop
   f934
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/name.rkt:77:0: register-name-sc
   f952
   f794
   /usr/share/racket/collects/racket/private/map.rkt:40:19: loop
   /usr/share/racket/collects/racket/private/map.rkt:35:13: map
   f1476
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/static-contracts/combinators/name.rkt:77:0: register-name-sc
   f952
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/private/type-contract.rkt:287:2
   /usr/share/racket/pkgs/typed-racket-lib/typed-racket/private/type-contract.rkt:84:0: generate-contract-def

Run the provided typed/racket reproduction first. Trace contract generation through typed-racket/static-contracts/instantiate.rkt, private/type-contract.rkt, and static-contracts/combinators/name.rkt, focusing on Refine handling. Done means define-predicate compiles without the car contract violation and rat? returns #t for the constructed rational.