; Standard Typed Lists Library
; Copyright (C) 2008-2014 Centaur Technology
;
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;   Centaur Technology Formal Verification Group
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; Original author: Jared Davis <jared@centtech.com>

(in-package "ACL2")
(include-book "std/util/deflist" :dir :system)

(in-theory (disable rational-listp))

(defsection std/typed-lists/rational-listp
  :parents (rational-listp)
  :short "Lemmas about @(see rational-listp) available in the @(see std/typed-lists)
library."

  :long "<p>Most of these are generated automatically with @(see
std::deflist).</p>"

  (std::deflist rational-listp (x)
                (rationalp x)
                :true-listp t
                :elementp-of-nil nil
                :already-definedp t
                ;; Set :parents to nil to avoid overwriting the built-in ACL2 documentation
                :parents nil)

  (defthm rational-listp-of-remove-equal
    ;; BOZO probably add to deflist
    (implies (rational-listp x)
             (rational-listp (remove-equal a x))))

  (defthm rational-listp-of-make-list-ac
    ;; BOZO probably silly given REPEAT as the normal form...
    (equal (rational-listp (make-list-ac n x ac))
           (and (rational-listp ac)
                (or (rationalp x)
                    (zp n)))))

  (defthm eqlable-listp-when-rational-listp
    ;; Useful for the guards of MEMBER on rational-listp's.
    ;; BOZO should this just be a TAU rule?
    (implies (rational-listp x)
             (eqlable-listp x))))
