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• Proof-utilities

No-duplicates-p

Signature

(no-duplicates-p l) → *

Arguments

l — Guard (true-listp l).

Definitions and Theorems

Function: no-duplicates-p

(defun no-duplicates-p (l)
  (declare (xargs :guard (true-listp l)))
  (let ((__function__ 'no-duplicates-p))
    (declare (ignorable __function__))
    (cond ((endp l) t)
          ((member-p (car l) (cdr l)) nil)
          (t (no-duplicates-p (cdr l))))))

Theorem: no-duplicates-p-and-append

(defthm no-duplicates-p-and-append
  (implies (no-duplicates-p (append a b))
           (and (no-duplicates-p a)
                (no-duplicates-p b)))
  :rule-classes (:forward-chaining :rewrite))