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Acre-internals

Undup

Signature
(undup x) → new-x
Arguments: x — Guard (true-listp x).
Returns: new-x — Type (true-listp new-x).

Definitions and Theorems

Function: undup

(defun undup (x)
  (declare (xargs :guard (true-listp x)))
  (let ((__function__ 'undup))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (car x)
                 (undup (remove-equal (car x) (cdr x)))))
         :exec (undup-exec x nil))))

Theorem: true-listp-of-undup

(defthm true-listp-of-undup
  (b* ((new-x (undup x)))
    (true-listp new-x))
  :rule-classes :rewrite)

Theorem: undup-exec-is-undup

(defthm undup-exec-is-undup
 (b* ((?new-x (undup-exec x acc)))
  (equal
    new-x
    (revappend (alist-keys acc)
               (undup (set-difference-equal x (alist-keys acc)))))))

Theorem: element-list-p-of-undup

(defthm element-list-p-of-undup
  (implies (acl2::element-list-p x)
           (acl2::element-list-p (undup x)))
  :rule-classes :rewrite)

Theorem: consp-of-undup

(defthm consp-of-undup
  (b* ((?new-x (undup x)))
    (iff (consp new-x) (consp x))))

Theorem: undup-of-remove

(defthm undup-of-remove
  (equal (remove k (undup x))
         (undup (remove k x))))

Theorem: undup-of-undup

(defthm undup-of-undup
  (equal (undup (undup x)) (undup x)))

Theorem: undup-of-append

(defthm undup-of-append
  (equal (undup (append x y))
         (append (undup x)
                 (undup (set-difference$ y x)))))

Theorem: member-of-undup

(defthm member-of-undup
  (iff (member k (undup x)) (member k x)))

Theorem: undup-under-set-equiv

(defthm undup-under-set-equiv
  (set-equiv (undup x) x))

Theorem: undup-of-set-difference

(defthm undup-of-set-difference
  (equal (undup (set-difference$ x y))
         (set-difference$ (undup x) y)))

Theorem: undup-of-list-fix-x

(defthm undup-of-list-fix-x
  (equal (undup (list-fix x)) (undup x)))

Theorem: undup-list-equiv-congruence-on-x

(defthm undup-list-equiv-congruence-on-x
  (implies (list-equiv x x-equiv)
           (equal (undup x) (undup x-equiv)))
  :rule-classes :congruence)