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Tree-list-tuple4

Tree-list-tuple4p

Recognizer for tree-list-tuple4 structures.

Signature
(tree-list-tuple4p x) → *

Definitions and Theorems

Function: tree-list-tuple4p

(defun tree-list-tuple4p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'tree-list-tuple4p))
    (declare (ignorable __function__))
    (and (mbe :logic (and (alistp x)
                          (equal (strip-cars x)
                                 '(1st 2nd 3rd 4th)))
              :exec (fty::alist-with-carsp x '(1st 2nd 3rd 4th)))
         (b* ((1st (cdr (std::da-nth 0 x)))
              (2nd (cdr (std::da-nth 1 x)))
              (3rd (cdr (std::da-nth 2 x)))
              (4th (cdr (std::da-nth 3 x))))
           (and (tree-listp 1st)
                (tree-listp 2nd)
                (tree-listp 3rd)
                (tree-listp 4th))))))

Theorem: consp-when-tree-list-tuple4p

(defthm consp-when-tree-list-tuple4p
  (implies (tree-list-tuple4p x)
           (consp x))
  :rule-classes :compound-recognizer)