symbol-listp

(in-package "ACL2")

(defsection std/typed-lists/symbol-listp
  :parents (std/typed-lists symbol-listp)
  :short "Lemmas about @(see symbol-listp) available in the @(see
std/typed-lists) library."
  :long "<p>Most of these are generated automatically with @(see
std::deflist).</p>"
  (deflist symbol-listp
    (x)
    (symbolp x)
    :true-listp t
    :elementp-of-nil t
    :already-definedp t
    :parents nil)
  (defthm true-listp-when-symbol-listp-rewrite-backchain-1
    (implies (symbol-listp x) (true-listp x))
    :rule-classes ((:rewrite :backchain-limit-lst 1)))
  (defthmd true-listp-when-symbol-listp-rewrite
    (implies (symbol-listp x) (true-listp x)))
  (defthm symbol-listp-of-remove-equal
    (implies (symbol-listp x) (symbol-listp (remove-equal a x))))
  (defthm symbol-listp-of-remove1-equal
    (implies (symbol-listp x)
      (symbol-listp (remove1-equal a x))))
  (defthm symbol-listp-of-make-list-ac
    (equal (symbol-listp (make-list-ac n x ac))
      (and (symbol-listp ac) (or (symbolp x) (zp n)))))
  (defthm eqlable-listp-when-symbol-listp
    (implies (symbol-listp x) (eqlable-listp x))))