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• Vl-paramdecloverridelist-p

Vl-paramdecloverridelist-p-basics

Basic theorems about vl-paramdecloverridelist-p, generated by deflist.

Definitions and Theorems

Theorem: vl-paramdecloverridelist-p-of-cons

(defthm vl-paramdecloverridelist-p-of-cons
  (equal (vl-paramdecloverridelist-p (cons acl2::a acl2::x))
         (and (vl-paramdecloverride-p acl2::a)
              (vl-paramdecloverridelist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-cdr-when-vl-paramdecloverridelist-p

(defthm
  vl-paramdecloverridelist-p-of-cdr-when-vl-paramdecloverridelist-p
  (implies (vl-paramdecloverridelist-p (double-rewrite acl2::x))
           (vl-paramdecloverridelist-p (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-when-not-consp

(defthm vl-paramdecloverridelist-p-when-not-consp
  (implies (not (consp acl2::x))
           (vl-paramdecloverridelist-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverride-p-of-car-when-vl-paramdecloverridelist-p

(defthm
      vl-paramdecloverride-p-of-car-when-vl-paramdecloverridelist-p
  (implies (vl-paramdecloverridelist-p acl2::x)
           (iff (vl-paramdecloverride-p (car acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-append

(defthm vl-paramdecloverridelist-p-of-append
  (equal (vl-paramdecloverridelist-p (append acl2::a acl2::b))
         (and (vl-paramdecloverridelist-p acl2::a)
              (vl-paramdecloverridelist-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-list-fix

(defthm vl-paramdecloverridelist-p-of-list-fix
  (equal (vl-paramdecloverridelist-p (list-fix acl2::x))
         (vl-paramdecloverridelist-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-sfix

(defthm vl-paramdecloverridelist-p-of-sfix
  (iff (vl-paramdecloverridelist-p (sfix acl2::x))
       (or (vl-paramdecloverridelist-p acl2::x)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-insert

(defthm vl-paramdecloverridelist-p-of-insert
  (iff (vl-paramdecloverridelist-p (insert acl2::a acl2::x))
       (and (vl-paramdecloverridelist-p (sfix acl2::x))
            (vl-paramdecloverride-p acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-delete

(defthm vl-paramdecloverridelist-p-of-delete
  (implies (vl-paramdecloverridelist-p acl2::x)
           (vl-paramdecloverridelist-p (delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-mergesort

(defthm vl-paramdecloverridelist-p-of-mergesort
  (iff (vl-paramdecloverridelist-p (mergesort acl2::x))
       (vl-paramdecloverridelist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-union

(defthm vl-paramdecloverridelist-p-of-union
  (iff (vl-paramdecloverridelist-p (union acl2::x acl2::y))
       (and (vl-paramdecloverridelist-p (sfix acl2::x))
            (vl-paramdecloverridelist-p (sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-intersect-1

(defthm vl-paramdecloverridelist-p-of-intersect-1
  (implies (vl-paramdecloverridelist-p acl2::x)
           (vl-paramdecloverridelist-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-intersect-2

(defthm vl-paramdecloverridelist-p-of-intersect-2
  (implies (vl-paramdecloverridelist-p acl2::y)
           (vl-paramdecloverridelist-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-difference

(defthm vl-paramdecloverridelist-p-of-difference
 (implies (vl-paramdecloverridelist-p acl2::x)
          (vl-paramdecloverridelist-p (difference acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-duplicated-members

(defthm vl-paramdecloverridelist-p-of-duplicated-members
 (implies (vl-paramdecloverridelist-p acl2::x)
          (vl-paramdecloverridelist-p (duplicated-members acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-rev

(defthm vl-paramdecloverridelist-p-of-rev
  (equal (vl-paramdecloverridelist-p (rev acl2::x))
         (vl-paramdecloverridelist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-rcons

(defthm vl-paramdecloverridelist-p-of-rcons
  (iff (vl-paramdecloverridelist-p (acl2::rcons acl2::a acl2::x))
       (and (vl-paramdecloverride-p acl2::a)
            (vl-paramdecloverridelist-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverride-p-when-member-equal-of-vl-paramdecloverridelist-p

(defthm
 vl-paramdecloverride-p-when-member-equal-of-vl-paramdecloverridelist-p
 (and (implies (and (member-equal acl2::a acl2::x)
                    (vl-paramdecloverridelist-p acl2::x))
               (vl-paramdecloverride-p acl2::a))
      (implies (and (vl-paramdecloverridelist-p acl2::x)
                    (member-equal acl2::a acl2::x))
               (vl-paramdecloverride-p acl2::a)))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-when-subsetp-equal

(defthm vl-paramdecloverridelist-p-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (vl-paramdecloverridelist-p acl2::y))
                (vl-paramdecloverridelist-p acl2::x))
       (implies (and (vl-paramdecloverridelist-p acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (vl-paramdecloverridelist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-set-equiv-congruence

(defthm vl-paramdecloverridelist-p-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (vl-paramdecloverridelist-p acl2::x)
                  (vl-paramdecloverridelist-p acl2::y)))
  :rule-classes :congruence)

Theorem: vl-paramdecloverridelist-p-of-set-difference-equal

(defthm vl-paramdecloverridelist-p-of-set-difference-equal
  (implies (vl-paramdecloverridelist-p acl2::x)
           (vl-paramdecloverridelist-p
                (set-difference-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-intersection-equal-1

(defthm vl-paramdecloverridelist-p-of-intersection-equal-1
 (implies
  (vl-paramdecloverridelist-p (double-rewrite acl2::x))
  (vl-paramdecloverridelist-p (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-intersection-equal-2

(defthm vl-paramdecloverridelist-p-of-intersection-equal-2
 (implies
  (vl-paramdecloverridelist-p (double-rewrite acl2::y))
  (vl-paramdecloverridelist-p (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-union-equal

(defthm vl-paramdecloverridelist-p-of-union-equal
 (equal (vl-paramdecloverridelist-p (union-equal acl2::x acl2::y))
        (and (vl-paramdecloverridelist-p (list-fix acl2::x))
             (vl-paramdecloverridelist-p (double-rewrite acl2::y))))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-take

(defthm vl-paramdecloverridelist-p-of-take
  (implies (vl-paramdecloverridelist-p (double-rewrite acl2::x))
           (iff (vl-paramdecloverridelist-p (take acl2::n acl2::x))
                (or (vl-paramdecloverride-p nil)
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-repeat

(defthm vl-paramdecloverridelist-p-of-repeat
  (iff (vl-paramdecloverridelist-p (repeat acl2::n acl2::x))
       (or (vl-paramdecloverride-p acl2::x)
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverride-p-of-nth-when-vl-paramdecloverridelist-p

(defthm
      vl-paramdecloverride-p-of-nth-when-vl-paramdecloverridelist-p
  (implies (vl-paramdecloverridelist-p acl2::x)
           (iff (vl-paramdecloverride-p (nth acl2::n acl2::x))
                (< (nfix acl2::n) (len acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-update-nth

(defthm vl-paramdecloverridelist-p-of-update-nth
 (implies
  (vl-paramdecloverridelist-p (double-rewrite acl2::x))
  (iff
   (vl-paramdecloverridelist-p (update-nth acl2::n acl2::y acl2::x))
   (and (vl-paramdecloverride-p acl2::y)
        (or (<= (nfix acl2::n) (len acl2::x))
            (vl-paramdecloverride-p nil)))))
 :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-butlast

(defthm vl-paramdecloverridelist-p-of-butlast
  (implies (vl-paramdecloverridelist-p (double-rewrite acl2::x))
           (vl-paramdecloverridelist-p (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-nthcdr

(defthm vl-paramdecloverridelist-p-of-nthcdr
  (implies (vl-paramdecloverridelist-p (double-rewrite acl2::x))
           (vl-paramdecloverridelist-p (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-last

(defthm vl-paramdecloverridelist-p-of-last
  (implies (vl-paramdecloverridelist-p (double-rewrite acl2::x))
           (vl-paramdecloverridelist-p (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-remove

(defthm vl-paramdecloverridelist-p-of-remove
  (implies (vl-paramdecloverridelist-p acl2::x)
           (vl-paramdecloverridelist-p (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-paramdecloverridelist-p-of-revappend

(defthm vl-paramdecloverridelist-p-of-revappend
  (equal (vl-paramdecloverridelist-p (revappend acl2::x acl2::y))
         (and (vl-paramdecloverridelist-p (list-fix acl2::x))
              (vl-paramdecloverridelist-p acl2::y)))
  :rule-classes ((:rewrite)))