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Signed-format

Signed-formatp

Recognizer for signed-format structures.

Signature
(signed-formatp x) → *

Definitions and Theorems

Function: signed-formatp

(defun signed-formatp (x)
  (declare (xargs :guard t))
  (and (consp x)
       (cond ((or (atom x)
                  (eq (car x) :sign-magnitude))
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 0)
                   (b* nil t)))
             ((eq (car x) :ones-complement)
              (and (true-listp (cdr x))
                   (eql (len (cdr x)) 0)
                   (b* nil t)))
             (t (and (eq (car x) :twos-complement)
                     (and (true-listp (cdr x))
                          (eql (len (cdr x)) 0))
                     (b* nil t))))))

Theorem: consp-when-signed-formatp

(defthm consp-when-signed-formatp
  (implies (signed-formatp x) (consp x))
  :rule-classes :compound-recognizer)