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Longest-common-prefix-list

(longest-common-prefix-list x) returns the longest list, p, such that p is a prefix of every list in x.

Signature

(longest-common-prefix-list x) → *

See also longest-common-prefix.

Definitions and Theorems

Function: longest-common-prefix-list

(defun longest-common-prefix-list (x)
 (declare (xargs :guard t))
 (let ((__function__ 'longest-common-prefix-list))
  (declare (ignorable __function__))
  (cond
   ((atom x) nil)
   ((atom (cdr x)) (list-fix (car x)))
   (t
    (longest-common-prefix (first x)
                           (longest-common-prefix-list (cdr x)))))))

Theorem: true-listp-of-longest-common-prefix-list

(defthm true-listp-of-longest-common-prefix-list
  (true-listp (longest-common-prefix-list x))
  :rule-classes :type-prescription)

Theorem: string-listp-of-longest-common-prefix-list

(defthm string-listp-of-longest-common-prefix-list
  (implies (string-list-listp x)
           (string-listp (longest-common-prefix-list x))))

Theorem: longest-common-prefix-list-of-list-fix

(defthm longest-common-prefix-list-of-list-fix
  (equal (longest-common-prefix-list (list-fix x))
         (longest-common-prefix-list x)))

Theorem: prefix-of-eachp-of-longest-common-prefix-list

(defthm prefix-of-eachp-of-longest-common-prefix-list
  (prefix-of-eachp (longest-common-prefix-list x)
                   x))