integer-listp

(in-package "ACL2")

(defsection std/typed-lists/integer-listp
  :parents (integer-listp)
  :short "Lemmas about @(see integer-listp) available in the @(see std/typed-lists)
library."
  :long "<p>Most of these are generated automatically with @(see
std::deflist).</p>"
  (deflist integer-listp
    (x)
    (integerp x)
    :true-listp t
    :elementp-of-nil nil
    :already-definedp t
    :parents nil)
  (defthm integer-listp-of-remove-equal
    (implies (integer-listp x)
      (integer-listp (remove-equal a x))))
  (defthm integer-listp-of-make-list-ac
    (equal (integer-listp (make-list-ac n x ac))
      (and (integer-listp ac) (or (integerp x) (zp n)))))
  (defthm eqlable-listp-when-integer-listp
    (implies (integer-listp x) (eqlable-listp x))))