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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))
  (let ((__function__ 'signed-formatp))
    (declare (ignorable __function__))
    (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)