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• Var-decl-map

Var-decl-map-p

Recognizer for var-decl-map.

Signature

(var-decl-map-p x) → *

Definitions and Theorems

Function: var-decl-map-p

(defun var-decl-map-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'var-decl-map-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (svar-p (caar x))
           (wire-p (cdar x))
           (var-decl-map-p (cdr x))))))

Theorem: var-decl-map-p-of-union-equal

(defthm var-decl-map-p-of-union-equal
  (equal (var-decl-map-p (union-equal x y))
         (and (var-decl-map-p (list-fix x))
              (var-decl-map-p (double-rewrite y))))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-intersection-equal-2

(defthm var-decl-map-p-of-intersection-equal-2
  (implies (var-decl-map-p (double-rewrite y))
           (var-decl-map-p (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-intersection-equal-1

(defthm var-decl-map-p-of-intersection-equal-1
  (implies (var-decl-map-p (double-rewrite x))
           (var-decl-map-p (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-set-difference-equal

(defthm var-decl-map-p-of-set-difference-equal
  (implies (var-decl-map-p x)
           (var-decl-map-p (set-difference-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-when-subsetp-equal

(defthm var-decl-map-p-when-subsetp-equal
  (and (implies (and (subsetp-equal x y)
                     (var-decl-map-p y))
                (equal (var-decl-map-p x)
                       (true-listp x)))
       (implies (and (var-decl-map-p y)
                     (subsetp-equal x y))
                (equal (var-decl-map-p x)
                       (true-listp x))))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-rcons

(defthm var-decl-map-p-of-rcons
  (iff (var-decl-map-p (acl2::rcons acl2::a x))
       (and (and (consp acl2::a)
                 (svar-p (car acl2::a))
                 (wire-p (cdr acl2::a)))
            (var-decl-map-p (list-fix x))))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-take

(defthm var-decl-map-p-of-take
  (implies (var-decl-map-p (double-rewrite x))
           (iff (var-decl-map-p (take acl2::n x))
                (or (and (consp nil)
                         (svar-p (car nil))
                         (wire-p (cdr nil)))
                    (<= (nfix acl2::n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-append

(defthm var-decl-map-p-of-append
  (equal (var-decl-map-p (append acl2::a acl2::b))
         (and (var-decl-map-p (list-fix acl2::a))
              (var-decl-map-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-repeat

(defthm var-decl-map-p-of-repeat
  (iff (var-decl-map-p (repeat acl2::n x))
       (or (and (consp x)
                (svar-p (car x))
                (wire-p (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-rev

(defthm var-decl-map-p-of-rev
  (equal (var-decl-map-p (rev x))
         (var-decl-map-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-list-fix

(defthm var-decl-map-p-of-list-fix
  (implies (var-decl-map-p x)
           (var-decl-map-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-var-decl-map-p-compound-recognizer

(defthm true-listp-when-var-decl-map-p-compound-recognizer
  (implies (var-decl-map-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: var-decl-map-p-when-not-consp

(defthm var-decl-map-p-when-not-consp
  (implies (not (consp x))
           (equal (var-decl-map-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-cdr-when-var-decl-map-p

(defthm var-decl-map-p-of-cdr-when-var-decl-map-p
  (implies (var-decl-map-p (double-rewrite x))
           (var-decl-map-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-cons

(defthm var-decl-map-p-of-cons
  (equal (var-decl-map-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (svar-p (car acl2::a))
                   (wire-p (cdr acl2::a)))
              (var-decl-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-remove-assoc

(defthm var-decl-map-p-of-remove-assoc
  (implies (var-decl-map-p x)
           (var-decl-map-p (remove-assoc-equal acl2::name x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-put-assoc

(defthm var-decl-map-p-of-put-assoc
 (implies
      (and (var-decl-map-p x))
      (iff (var-decl-map-p (put-assoc-equal acl2::name acl2::val x))
           (and (svar-p acl2::name)
                (wire-p acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-fast-alist-clean

(defthm var-decl-map-p-of-fast-alist-clean
  (implies (var-decl-map-p x)
           (var-decl-map-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-hons-shrink-alist

(defthm var-decl-map-p-of-hons-shrink-alist
  (implies (and (var-decl-map-p x)
                (var-decl-map-p y))
           (var-decl-map-p (hons-shrink-alist x y)))
  :rule-classes ((:rewrite)))

Theorem: var-decl-map-p-of-hons-acons

(defthm var-decl-map-p-of-hons-acons
  (equal (var-decl-map-p (hons-acons acl2::a acl2::n x))
         (and (svar-p acl2::a)
              (wire-p acl2::n)
              (var-decl-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: wire-p-of-cdr-of-hons-assoc-equal-when-var-decl-map-p

(defthm wire-p-of-cdr-of-hons-assoc-equal-when-var-decl-map-p
  (implies (var-decl-map-p x)
           (iff (wire-p (cdr (hons-assoc-equal acl2::k x)))
                (or (hons-assoc-equal acl2::k x)
                    (wire-p nil))))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-var-decl-map-p-rewrite

(defthm alistp-when-var-decl-map-p-rewrite
  (implies (var-decl-map-p x) (alistp x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-var-decl-map-p

(defthm alistp-when-var-decl-map-p
  (implies (var-decl-map-p x) (alistp x))
  :rule-classes :tau-system)

Theorem: wire-p-of-cdar-when-var-decl-map-p

(defthm wire-p-of-cdar-when-var-decl-map-p
  (implies (var-decl-map-p x)
           (iff (wire-p (cdar x))
                (or (consp x) (wire-p nil))))
  :rule-classes ((:rewrite)))

Theorem: svar-p-of-caar-when-var-decl-map-p

(defthm svar-p-of-caar-when-var-decl-map-p
  (implies (var-decl-map-p x)
           (iff (svar-p (caar x))
                (or (consp x) (svar-p nil))))
  :rule-classes ((:rewrite)))