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Undocumented

Ecut-wirename-alistp

(ecut-wirename-alistp x) recognizes association lists where every key satisfies symbolp and each value satisfies ecutnames-p.

This is an ordinary std::defalist.

Function: ecut-wirename-alistp

(defun ecut-wirename-alistp (x)
       (declare (xargs :guard t))
       (if (consp x)
           (and (consp (car x))
                (symbolp (caar x))
                (ecutnames-p (cdar x))
                (ecut-wirename-alistp (cdr x)))
           t))

Definitions and Theorems

Function: ecut-wirename-alistp

(defun ecut-wirename-alistp (x)
       (declare (xargs :guard t))
       (if (consp x)
           (and (consp (car x))
                (symbolp (caar x))
                (ecutnames-p (cdar x))
                (ecut-wirename-alistp (cdr x)))
           t))

Theorem: ecut-wirename-alistp-of-revappend

(defthm ecut-wirename-alistp-of-revappend
        (equal (ecut-wirename-alistp (revappend x y))
               (and (ecut-wirename-alistp (list-fix x))
                    (ecut-wirename-alistp y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-remove

(defthm ecut-wirename-alistp-of-remove
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (remove a x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-last

(defthm ecut-wirename-alistp-of-last
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (ecut-wirename-alistp (last x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-nthcdr

(defthm ecut-wirename-alistp-of-nthcdr
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (ecut-wirename-alistp (nthcdr n x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-butlast

(defthm ecut-wirename-alistp-of-butlast
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (ecut-wirename-alistp (butlast x n)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-update-nth

(defthm ecut-wirename-alistp-of-update-nth
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (iff (ecut-wirename-alistp (update-nth n y x))
                      (and (and (consp y)
                                (symbolp (car y))
                                (ecutnames-p (cdr y)))
                           (or (<= (nfix n) (len x))
                               (and (consp nil)
                                    (symbolp (car nil))
                                    (ecutnames-p (cdr nil)))))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-repeat

(defthm ecut-wirename-alistp-of-repeat
        (iff (ecut-wirename-alistp (repeat n x))
             (or (and (consp x)
                      (symbolp (car x))
                      (ecutnames-p (cdr x)))
                 (zp n)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-take

(defthm ecut-wirename-alistp-of-take
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (iff (ecut-wirename-alistp (take n x))
                      (or (and (consp nil)
                               (symbolp (car nil))
                               (ecutnames-p (cdr nil)))
                          (<= (nfix n) (len x)))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-union-equal

(defthm ecut-wirename-alistp-of-union-equal
        (equal (ecut-wirename-alistp (union-equal x y))
               (and (ecut-wirename-alistp (list-fix x))
                    (ecut-wirename-alistp (double-rewrite y))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-intersection-equal-2

(defthm ecut-wirename-alistp-of-intersection-equal-2
        (implies (ecut-wirename-alistp (double-rewrite y))
                 (ecut-wirename-alistp (intersection-equal x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-intersection-equal-1

(defthm ecut-wirename-alistp-of-intersection-equal-1
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (ecut-wirename-alistp (intersection-equal x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-set-difference-equal

(defthm ecut-wirename-alistp-of-set-difference-equal
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (set-difference-equal x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-set-equiv-congruence

(defthm ecut-wirename-alistp-set-equiv-congruence
        (implies (set-equiv x y)
                 (equal (ecut-wirename-alistp x)
                        (ecut-wirename-alistp y)))
        :rule-classes :congruence)

Theorem: ecut-wirename-alistp-when-subsetp-equal

(defthm ecut-wirename-alistp-when-subsetp-equal
        (and (implies (and (subsetp-equal x y)
                           (ecut-wirename-alistp y))
                      (ecut-wirename-alistp x))
             (implies (and (ecut-wirename-alistp y)
                           (subsetp-equal x y))
                      (ecut-wirename-alistp x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-rcons

(defthm ecut-wirename-alistp-of-rcons
        (iff (ecut-wirename-alistp (rcons a x))
             (and (and (consp a)
                       (symbolp (car a))
                       (ecutnames-p (cdr a)))
                  (ecut-wirename-alistp (list-fix x))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-rev

(defthm ecut-wirename-alistp-of-rev
        (equal (ecut-wirename-alistp (rev x))
               (ecut-wirename-alistp (list-fix x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-duplicated-members

(defthm ecut-wirename-alistp-of-duplicated-members
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (duplicated-members x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-difference

(defthm ecut-wirename-alistp-of-difference
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (set::difference x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-intersect-2

(defthm ecut-wirename-alistp-of-intersect-2
        (implies (ecut-wirename-alistp y)
                 (ecut-wirename-alistp (set::intersect x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-intersect-1

(defthm ecut-wirename-alistp-of-intersect-1
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (set::intersect x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-union

(defthm ecut-wirename-alistp-of-union
        (iff (ecut-wirename-alistp (set::union x y))
             (and (ecut-wirename-alistp (set::sfix x))
                  (ecut-wirename-alistp (set::sfix y))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-mergesort

(defthm ecut-wirename-alistp-of-mergesort
        (iff (ecut-wirename-alistp (set::mergesort x))
             (ecut-wirename-alistp (list-fix x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-delete

(defthm ecut-wirename-alistp-of-delete
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (set::delete k x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-insert

(defthm ecut-wirename-alistp-of-insert
        (iff (ecut-wirename-alistp (set::insert a x))
             (and (ecut-wirename-alistp (set::sfix x))
                  (and (consp a)
                       (symbolp (car a))
                       (ecutnames-p (cdr a)))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-sfix

(defthm ecut-wirename-alistp-of-sfix
        (iff (ecut-wirename-alistp (set::sfix x))
             (or (ecut-wirename-alistp x)
                 (not (set::setp x))))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-list-fix

(defthm ecut-wirename-alistp-of-list-fix
        (equal (ecut-wirename-alistp (list-fix x))
               (ecut-wirename-alistp x))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-append

(defthm ecut-wirename-alistp-of-append
        (equal (ecut-wirename-alistp (append a b))
               (and (ecut-wirename-alistp a)
                    (ecut-wirename-alistp b)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-when-not-consp

(defthm ecut-wirename-alistp-when-not-consp
        (implies (not (consp x))
                 (ecut-wirename-alistp x))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-cdr-when-ecut-wirename-alistp

(defthm ecut-wirename-alistp-of-cdr-when-ecut-wirename-alistp
        (implies (ecut-wirename-alistp (double-rewrite x))
                 (ecut-wirename-alistp (cdr x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-cons

(defthm ecut-wirename-alistp-of-cons
        (equal (ecut-wirename-alistp (cons a x))
               (and (and (consp a)
                         (symbolp (car a))
                         (ecutnames-p (cdr a)))
                    (ecut-wirename-alistp x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-make-fal

(defthm ecut-wirename-alistp-of-make-fal
        (implies (and (ecut-wirename-alistp x)
                      (ecut-wirename-alistp y))
                 (ecut-wirename-alistp (make-fal x y)))
        :rule-classes ((:rewrite)))

Theorem: ecutnames-p-of-cdr-when-member-equal-of-ecut-wirename-alistp

(defthm ecutnames-p-of-cdr-when-member-equal-of-ecut-wirename-alistp
        (and (implies (and (ecut-wirename-alistp x)
                           (member-equal a x))
                      (ecutnames-p (cdr a)))
             (implies (and (member-equal a x)
                           (ecut-wirename-alistp x))
                      (ecutnames-p (cdr a))))
        :rule-classes ((:rewrite)))

Theorem: symbolp-of-car-when-member-equal-of-ecut-wirename-alistp

(defthm symbolp-of-car-when-member-equal-of-ecut-wirename-alistp
        (and (implies (and (ecut-wirename-alistp x)
                           (member-equal a x))
                      (symbolp (car a)))
             (implies (and (member-equal a x)
                           (ecut-wirename-alistp x))
                      (symbolp (car a))))
        :rule-classes ((:rewrite)))

Theorem: consp-when-member-equal-of-ecut-wirename-alistp

(defthm consp-when-member-equal-of-ecut-wirename-alistp
        (implies (and (ecut-wirename-alistp x)
                      (member-equal a x))
                 (consp a))
        :rule-classes
        ((:rewrite :backchain-limit-lst (0 0))
         (:rewrite :backchain-limit-lst (0 0)
                   :corollary (implies (if (member-equal a x)
                                           (ecut-wirename-alistp x)
                                           'nil)
                                       (consp a)))))

Theorem: ecut-wirename-alistp-of-fast-alist-clean

(defthm ecut-wirename-alistp-of-fast-alist-clean
        (implies (ecut-wirename-alistp x)
                 (ecut-wirename-alistp (fast-alist-clean x)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-hons-shrink-alist

(defthm ecut-wirename-alistp-of-hons-shrink-alist
        (implies (and (ecut-wirename-alistp x)
                      (ecut-wirename-alistp y))
                 (ecut-wirename-alistp (hons-shrink-alist x y)))
        :rule-classes ((:rewrite)))

Theorem: ecut-wirename-alistp-of-hons-acons

(defthm ecut-wirename-alistp-of-hons-acons
        (equal (ecut-wirename-alistp (hons-acons a n x))
               (and (symbolp a)
                    (ecutnames-p n)
                    (ecut-wirename-alistp x)))
        :rule-classes ((:rewrite)))

Theorem: ecutnames-p-of-cdr-of-hons-assoc-equal-when-ecut-wirename-alistp

(defthm
    ecutnames-p-of-cdr-of-hons-assoc-equal-when-ecut-wirename-alistp
    (implies (ecut-wirename-alistp x)
             (iff (ecutnames-p (cdr (hons-assoc-equal k x)))
                  (hons-assoc-equal k x)))
    :rule-classes ((:rewrite)))

Theorem: ecutnames-p-of-cdar-when-ecut-wirename-alistp

(defthm ecutnames-p-of-cdar-when-ecut-wirename-alistp
        (implies (ecut-wirename-alistp x)
                 (iff (ecutnames-p (cdar x)) (consp x)))
        :rule-classes ((:rewrite)))

Theorem: symbolp-of-caar-when-ecut-wirename-alistp

(defthm symbolp-of-caar-when-ecut-wirename-alistp
        (implies (ecut-wirename-alistp x)
                 (symbolp (caar x)))
        :rule-classes ((:rewrite)))