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Type-checking

Funparam-list-to-var/const-sinfo-list

Lift funparam-to-var/const-sinfo to lists.

Signature
(funparam-list-to-var/const-sinfo-list x) → infos
Returns: infos — Type (var/const-sinfo-listp infos).

Definitions and Theorems

Function: funparam-list-to-var/const-sinfo-list-exec

(defun funparam-list-to-var/const-sinfo-list-exec (x acc)
  (declare (xargs :guard (funparam-listp x)))
  (let ((__function__ 'funparam-list-to-var/const-sinfo-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (funparam-list-to-var/const-sinfo-list-exec
             (cdr x)
             (cons (funparam-to-var/const-sinfo (car x))
                   acc))
      acc)))

Function: funparam-list-to-var/const-sinfo-list-nrev

(defun funparam-list-to-var/const-sinfo-list-nrev (x acl2::nrev)
 (declare (xargs :stobjs (acl2::nrev)))
 (declare (xargs :guard (funparam-listp x)))
 (let ((__function__ 'funparam-list-to-var/const-sinfo-list-nrev))
  (declare (ignorable __function__))
  (if (atom x)
      (acl2::nrev-fix acl2::nrev)
   (let ((acl2::nrev
              (acl2::nrev-push (funparam-to-var/const-sinfo (car x))
                               acl2::nrev)))
     (funparam-list-to-var/const-sinfo-list-nrev (cdr x)
                                                 acl2::nrev)))))

Function: funparam-list-to-var/const-sinfo-list

(defun funparam-list-to-var/const-sinfo-list (x)
 (declare (xargs :guard (funparam-listp x)))
 (let ((__function__ 'funparam-list-to-var/const-sinfo-list))
  (declare (ignorable __function__))
  (mbe
   :logic
   (if (consp x)
       (cons (funparam-to-var/const-sinfo (car x))
             (funparam-list-to-var/const-sinfo-list (cdr x)))
     nil)
   :exec
   (if (atom x)
       nil
    (acl2::with-local-nrev
      (funparam-list-to-var/const-sinfo-list-nrev x acl2::nrev))))))

Theorem: var/const-sinfo-listp-of-funparam-list-to-var/const-sinfo-list

(defthm
     var/const-sinfo-listp-of-funparam-list-to-var/const-sinfo-list
  (b* ((infos (funparam-list-to-var/const-sinfo-list x)))
    (var/const-sinfo-listp infos))
  :rule-classes :rewrite)

Theorem: funparam-list-to-var/const-sinfo-list-nrev-removal

(defthm funparam-list-to-var/const-sinfo-list-nrev-removal
 (equal
     (funparam-list-to-var/const-sinfo-list-nrev acl2::x acl2::nrev)
     (append acl2::nrev
             (funparam-list-to-var/const-sinfo-list acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-exec-removal

(defthm funparam-list-to-var/const-sinfo-list-exec-removal
 (equal
      (funparam-list-to-var/const-sinfo-list-exec acl2::x acl2::acc)
      (revappend (funparam-list-to-var/const-sinfo-list acl2::x)
                 acl2::acc))
 :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-take

(defthm funparam-list-to-var/const-sinfo-list-of-take
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
      (funparam-list-to-var/const-sinfo-list (take acl2::n acl2::x))
      (take acl2::n
            (funparam-list-to-var/const-sinfo-list acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-funparam-list-to-var/const-sinfo-list

(defthm
    set-equiv-congruence-over-funparam-list-to-var/const-sinfo-list
  (implies
       (set-equiv acl2::x acl2::y)
       (set-equiv (funparam-list-to-var/const-sinfo-list acl2::x)
                  (funparam-list-to-var/const-sinfo-list acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-funparam-list-to-var/const-sinfo-list-when-subsetp

(defthm
      subsetp-of-funparam-list-to-var/const-sinfo-list-when-subsetp
 (implies (subsetp acl2::x acl2::y)
          (subsetp (funparam-list-to-var/const-sinfo-list acl2::x)
                   (funparam-list-to-var/const-sinfo-list acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: member-of-funparam-to-var/const-sinfo-in-funparam-list-to-var/const-sinfo-list

(defthm
 member-of-funparam-to-var/const-sinfo-in-funparam-list-to-var/const-sinfo-list
 (implies (member acl2::k acl2::x)
          (member (funparam-to-var/const-sinfo acl2::k)
                  (funparam-list-to-var/const-sinfo-list acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-rev

(defthm funparam-list-to-var/const-sinfo-list-of-rev
  (equal (funparam-list-to-var/const-sinfo-list (rev acl2::x))
         (rev (funparam-list-to-var/const-sinfo-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-list-fix

(defthm funparam-list-to-var/const-sinfo-list-of-list-fix
  (equal (funparam-list-to-var/const-sinfo-list (list-fix acl2::x))
         (funparam-list-to-var/const-sinfo-list acl2::x))
  :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-append

(defthm funparam-list-to-var/const-sinfo-list-of-append
 (equal
    (funparam-list-to-var/const-sinfo-list (append acl2::a acl2::b))
    (append (funparam-list-to-var/const-sinfo-list acl2::a)
            (funparam-list-to-var/const-sinfo-list acl2::b)))
 :rule-classes ((:rewrite)))

Theorem: cdr-of-funparam-list-to-var/const-sinfo-list

(defthm cdr-of-funparam-list-to-var/const-sinfo-list
  (equal (cdr (funparam-list-to-var/const-sinfo-list acl2::x))
         (funparam-list-to-var/const-sinfo-list (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-funparam-list-to-var/const-sinfo-list

(defthm car-of-funparam-list-to-var/const-sinfo-list
  (equal (car (funparam-list-to-var/const-sinfo-list acl2::x))
         (and (consp acl2::x)
              (funparam-to-var/const-sinfo (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-under-iff

(defthm funparam-list-to-var/const-sinfo-list-under-iff
  (iff (funparam-list-to-var/const-sinfo-list acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-funparam-list-to-var/const-sinfo-list

(defthm consp-of-funparam-list-to-var/const-sinfo-list
  (equal (consp (funparam-list-to-var/const-sinfo-list acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-funparam-list-to-var/const-sinfo-list

(defthm len-of-funparam-list-to-var/const-sinfo-list
  (equal (len (funparam-list-to-var/const-sinfo-list acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-funparam-list-to-var/const-sinfo-list

(defthm true-listp-of-funparam-list-to-var/const-sinfo-list
  (true-listp (funparam-list-to-var/const-sinfo-list acl2::x))
  :rule-classes :type-prescription)

Theorem: funparam-list-to-var/const-sinfo-list-when-not-consp

(defthm funparam-list-to-var/const-sinfo-list-when-not-consp
  (implies (not (consp acl2::x))
           (equal (funparam-list-to-var/const-sinfo-list acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-cons

(defthm funparam-list-to-var/const-sinfo-list-of-cons
 (equal
      (funparam-list-to-var/const-sinfo-list (cons acl2::a acl2::b))
      (cons (funparam-to-var/const-sinfo acl2::a)
            (funparam-list-to-var/const-sinfo-list acl2::b)))
 :rule-classes ((:rewrite)))

Theorem: funparam-list-to-var/const-sinfo-list-of-funparam-list-fix-x

(defthm funparam-list-to-var/const-sinfo-list-of-funparam-list-fix-x
  (equal
       (funparam-list-to-var/const-sinfo-list (funparam-list-fix x))
       (funparam-list-to-var/const-sinfo-list x)))

Theorem: funparam-list-to-var/const-sinfo-list-funparam-list-equiv-congruence-on-x

(defthm
 funparam-list-to-var/const-sinfo-list-funparam-list-equiv-congruence-on-x
 (implies (funparam-list-equiv x x-equiv)
          (equal (funparam-list-to-var/const-sinfo-list x)
                 (funparam-list-to-var/const-sinfo-list x-equiv)))
 :rule-classes :congruence)