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Filepath-set

Filepath-setp

Recognizer for filepath-set.

Signature
(filepath-setp x) → *

Definitions and Theorems

Function: filepath-setp

(defun filepath-setp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (filepathp (car x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (acl2::fast-<< (car x) (cadr x))
                  (filepath-setp (cdr x)))))))

Theorem: booleanp-offilepath-setp

(defthm booleanp-offilepath-setp
  (booleanp (filepath-setp x)))

Theorem: setp-when-filepath-setp

(defthm setp-when-filepath-setp
  (implies (filepath-setp x) (setp x))
  :rule-classes (:rewrite))

Theorem: filepathp-of-head-when-filepath-setp

(defthm filepathp-of-head-when-filepath-setp
  (implies (filepath-setp x)
           (implies (not (emptyp x))
                    (filepathp (head x)))))

Theorem: filepath-setp-of-tail-when-filepath-setp

(defthm filepath-setp-of-tail-when-filepath-setp
  (implies (filepath-setp x)
           (filepath-setp (tail x))))

Theorem: filepath-setp-of-insert

(defthm filepath-setp-of-insert
  (equal (filepath-setp (insert a x))
         (and (filepathp a)
              (filepath-setp (sfix x)))))

Theorem: filepathp-when-in-filepath-setp-binds-free-x

(defthm filepathp-when-in-filepath-setp-binds-free-x
  (implies (and (in a x) (filepath-setp x))
           (filepathp a)))

Theorem: not-in-filepath-setp-when-not-filepathp

(defthm not-in-filepath-setp-when-not-filepathp
  (implies (and (filepath-setp x)
                (not (filepathp a)))
           (not (in a x))))

Theorem: filepath-setp-of-union

(defthm filepath-setp-of-union
  (equal (filepath-setp (union x y))
         (and (filepath-setp (sfix x))
              (filepath-setp (sfix y)))))

Theorem: filepath-setp-of-intersect

(defthm filepath-setp-of-intersect
  (implies (and (filepath-setp x)
                (filepath-setp y))
           (filepath-setp (intersect x y))))

Theorem: filepath-setp-of-difference

(defthm filepath-setp-of-difference
  (implies (filepath-setp x)
           (filepath-setp (difference x y))))

Theorem: filepath-setp-of-delete

(defthm filepath-setp-of-delete
  (implies (filepath-setp x)
           (filepath-setp (delete a x))))