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Lhbit

Lhbit-p

Recognizer for lhbit structures.

Signature
(lhbit-p x) → *

Definitions and Theorems

Function: lhbit-p

(defun lhbit-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'lhbit-p))
    (declare (ignorable __function__))
    (and (consp x)
         (cond ((or (atom x) (eq (car x) :z))
                (and (true-listp (cdr x))
                     (eql (len (cdr x)) 0)
                     (b* nil t)))
               (t (and (eq (car x) :var)
                       (and (std::prod-consp (cdr x)))
                       (b* ((name (std::prod-car (cdr x)))
                            (idx (std::prod-cdr (cdr x))))
                         (and (svar-p name) (natp idx)))))))))

Theorem: consp-when-lhbit-p

(defthm consp-when-lhbit-p
  (implies (lhbit-p x) (consp x))
  :rule-classes :compound-recognizer)