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Valid-defstatus

Valid-defstatusp

Recognizer for valid-defstatus structures.

Signature
(valid-defstatusp x) → *

Definitions and Theorems

Function: valid-defstatusp

(defun valid-defstatusp (x)
  (declare (xargs :guard t))
  (let ((__function__ 'valid-defstatusp))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :undefined))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               ((eq (car x) :tentative)
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :defined)
                       (and (true-listp (cdr x))
                            (eql (len (cdr x)) 0))
                       (b* nil t)))))))

Theorem: consp-when-valid-defstatusp

(defthm consp-when-valid-defstatusp
  (implies (valid-defstatusp x) (consp x))
  :rule-classes :compound-recognizer)