character-listp

(in-package "ACL2")

(defsection std/typed-lists/character-listp
  :parents (std/typed-lists character-listp)
  :short "Lemmas about @(see character-listp) available in the @(see
std/typed-lists) library."
  :long "<p>Most of these are generated automatically with @(see
std::deflist).</p>"
  (deflist character-listp
    (x)
    (characterp x)
    :true-listp t
    :elementp-of-nil nil
    :already-definedp t
    :parents nil)
  (defthm true-listp-when-character-listp-rewrite
    (implies (character-listp x) (true-listp x))
    :rule-classes ((:rewrite :backchain-limit-lst 1)))
  (defthm character-listp-of-remove-equal
    (implies (character-listp x)
      (character-listp (remove-equal a x))))
  (defthm character-listp-of-make-list-ac
    (equal (character-listp (make-list-ac n x ac))
      (and (character-listp ac) (or (characterp x) (zp n)))))
  (defthm eqlable-listp-when-character-listp
    (implies (character-listp x) (eqlable-listp x)))
  (defthm character-listp-of-rev
    (equal (character-listp (rev x))
      (character-listp (list-fix x)))
    :hints (("Goal" :induct (len x)))))