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• Vl-propportlist

Vl-propportlist-fix

(vl-propportlist-fix x) is a usual fty list fixing function.

Signature

(vl-propportlist-fix x) → fty::newx

Arguments

x — Guard (vl-propportlist-p x).

Returns

fty::newx — Type (vl-propportlist-p fty::newx).

In the logic, we apply vl-propport-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.

Definitions and Theorems

Function: vl-propportlist-fix$inline

(defun vl-propportlist-fix$inline (x)
       (declare (xargs :guard (vl-propportlist-p x)))
       (let ((__function__ 'vl-propportlist-fix))
            (declare (ignorable __function__))
            (mbe :logic (if (atom x)
                            x
                            (cons (vl-propport-fix (car x))
                                  (vl-propportlist-fix (cdr x))))
                 :exec x)))

Theorem: vl-propportlist-p-of-vl-propportlist-fix

(defthm vl-propportlist-p-of-vl-propportlist-fix
        (b* ((fty::newx (vl-propportlist-fix$inline x)))
            (vl-propportlist-p fty::newx))
        :rule-classes :rewrite)

Theorem: vl-propportlist-fix-when-vl-propportlist-p

(defthm vl-propportlist-fix-when-vl-propportlist-p
        (implies (vl-propportlist-p x)
                 (equal (vl-propportlist-fix x) x)))

Function: vl-propportlist-equiv$inline

(defun vl-propportlist-equiv$inline
       (acl2::x acl2::y)
       (declare (xargs :guard (and (vl-propportlist-p acl2::x)
                                   (vl-propportlist-p acl2::y))))
       (equal (vl-propportlist-fix acl2::x)
              (vl-propportlist-fix acl2::y)))

Theorem: vl-propportlist-equiv-is-an-equivalence

(defthm vl-propportlist-equiv-is-an-equivalence
        (and (booleanp (vl-propportlist-equiv x y))
             (vl-propportlist-equiv x x)
             (implies (vl-propportlist-equiv x y)
                      (vl-propportlist-equiv y x))
             (implies (and (vl-propportlist-equiv x y)
                           (vl-propportlist-equiv y z))
                      (vl-propportlist-equiv x z)))
        :rule-classes (:equivalence))

Theorem: vl-propportlist-equiv-implies-equal-vl-propportlist-fix-1

(defthm vl-propportlist-equiv-implies-equal-vl-propportlist-fix-1
        (implies (vl-propportlist-equiv acl2::x x-equiv)
                 (equal (vl-propportlist-fix acl2::x)
                        (vl-propportlist-fix x-equiv)))
        :rule-classes (:congruence))

Theorem: vl-propportlist-fix-under-vl-propportlist-equiv

(defthm vl-propportlist-fix-under-vl-propportlist-equiv
        (vl-propportlist-equiv (vl-propportlist-fix acl2::x)
                               acl2::x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-propportlist-fix-1-forward-to-vl-propportlist-equiv

(defthm
     equal-of-vl-propportlist-fix-1-forward-to-vl-propportlist-equiv
     (implies (equal (vl-propportlist-fix acl2::x)
                     acl2::y)
              (vl-propportlist-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

Theorem: equal-of-vl-propportlist-fix-2-forward-to-vl-propportlist-equiv

(defthm
     equal-of-vl-propportlist-fix-2-forward-to-vl-propportlist-equiv
     (implies (equal acl2::x (vl-propportlist-fix acl2::y))
              (vl-propportlist-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

Theorem: vl-propportlist-equiv-of-vl-propportlist-fix-1-forward

(defthm
     vl-propportlist-equiv-of-vl-propportlist-fix-1-forward
     (implies (vl-propportlist-equiv (vl-propportlist-fix acl2::x)
                                     acl2::y)
              (vl-propportlist-equiv acl2::x acl2::y))
     :rule-classes :forward-chaining)

Theorem: vl-propportlist-equiv-of-vl-propportlist-fix-2-forward

(defthm
  vl-propportlist-equiv-of-vl-propportlist-fix-2-forward
  (implies
       (vl-propportlist-equiv acl2::x (vl-propportlist-fix acl2::y))
       (vl-propportlist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: car-of-vl-propportlist-fix-x-under-vl-propport-equiv

(defthm car-of-vl-propportlist-fix-x-under-vl-propport-equiv
        (vl-propport-equiv (car (vl-propportlist-fix acl2::x))
                           (car acl2::x)))

Theorem: car-vl-propportlist-equiv-congruence-on-x-under-vl-propport-equiv

(defthm
   car-vl-propportlist-equiv-congruence-on-x-under-vl-propport-equiv
   (implies (vl-propportlist-equiv acl2::x x-equiv)
            (vl-propport-equiv (car acl2::x)
                               (car x-equiv)))
   :rule-classes :congruence)

Theorem: cdr-of-vl-propportlist-fix-x-under-vl-propportlist-equiv

(defthm cdr-of-vl-propportlist-fix-x-under-vl-propportlist-equiv
        (vl-propportlist-equiv (cdr (vl-propportlist-fix acl2::x))
                               (cdr acl2::x)))

Theorem: cdr-vl-propportlist-equiv-congruence-on-x-under-vl-propportlist-equiv

(defthm
 cdr-vl-propportlist-equiv-congruence-on-x-under-vl-propportlist-equiv
 (implies (vl-propportlist-equiv acl2::x x-equiv)
          (vl-propportlist-equiv (cdr acl2::x)
                                 (cdr x-equiv)))
 :rule-classes :congruence)

Theorem: cons-of-vl-propport-fix-x-under-vl-propportlist-equiv

(defthm
     cons-of-vl-propport-fix-x-under-vl-propportlist-equiv
     (vl-propportlist-equiv (cons (vl-propport-fix acl2::x) acl2::y)
                            (cons acl2::x acl2::y)))

Theorem: cons-vl-propport-equiv-congruence-on-x-under-vl-propportlist-equiv

(defthm
  cons-vl-propport-equiv-congruence-on-x-under-vl-propportlist-equiv
  (implies (vl-propport-equiv acl2::x x-equiv)
           (vl-propportlist-equiv (cons acl2::x acl2::y)
                                  (cons x-equiv acl2::y)))
  :rule-classes :congruence)

Theorem: cons-of-vl-propportlist-fix-y-under-vl-propportlist-equiv

(defthm
 cons-of-vl-propportlist-fix-y-under-vl-propportlist-equiv
 (vl-propportlist-equiv (cons acl2::x (vl-propportlist-fix acl2::y))
                        (cons acl2::x acl2::y)))

Theorem: cons-vl-propportlist-equiv-congruence-on-y-under-vl-propportlist-equiv

(defthm
 cons-vl-propportlist-equiv-congruence-on-y-under-vl-propportlist-equiv
 (implies (vl-propportlist-equiv acl2::y y-equiv)
          (vl-propportlist-equiv (cons acl2::x acl2::y)
                                 (cons acl2::x y-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-vl-propportlist-fix

(defthm consp-of-vl-propportlist-fix
        (equal (consp (vl-propportlist-fix acl2::x))
               (consp acl2::x)))

Theorem: vl-propportlist-fix-of-cons

(defthm vl-propportlist-fix-of-cons
        (equal (vl-propportlist-fix (cons a x))
               (cons (vl-propport-fix a)
                     (vl-propportlist-fix x))))

Theorem: len-of-vl-propportlist-fix

(defthm len-of-vl-propportlist-fix
        (equal (len (vl-propportlist-fix acl2::x))
               (len acl2::x)))

Theorem: vl-propportlist-fix-of-append

(defthm vl-propportlist-fix-of-append
        (equal (vl-propportlist-fix (append std::a std::b))
               (append (vl-propportlist-fix std::a)
                       (vl-propportlist-fix std::b))))

Theorem: vl-propportlist-fix-of-repeat

(defthm vl-propportlist-fix-of-repeat
        (equal (vl-propportlist-fix (repeat acl2::n acl2::x))
               (repeat acl2::n (vl-propport-fix acl2::x))))

Theorem: nth-of-vl-propportlist-fix

(defthm nth-of-vl-propportlist-fix
        (equal (nth acl2::n (vl-propportlist-fix acl2::x))
               (if (< (nfix acl2::n) (len acl2::x))
                   (vl-propport-fix (nth acl2::n acl2::x))
                   nil)))

Theorem: vl-propportlist-equiv-implies-vl-propportlist-equiv-append-1

(defthm
     vl-propportlist-equiv-implies-vl-propportlist-equiv-append-1
     (implies (vl-propportlist-equiv acl2::x fty::x-equiv)
              (vl-propportlist-equiv (append acl2::x acl2::y)
                                     (append fty::x-equiv acl2::y)))
     :rule-classes (:congruence))

Theorem: vl-propportlist-equiv-implies-vl-propportlist-equiv-append-2

(defthm
     vl-propportlist-equiv-implies-vl-propportlist-equiv-append-2
     (implies (vl-propportlist-equiv acl2::y fty::y-equiv)
              (vl-propportlist-equiv (append acl2::x acl2::y)
                                     (append acl2::x fty::y-equiv)))
     :rule-classes (:congruence))

Theorem: vl-propportlist-equiv-implies-vl-propportlist-equiv-nthcdr-2

(defthm vl-propportlist-equiv-implies-vl-propportlist-equiv-nthcdr-2
        (implies (vl-propportlist-equiv acl2::l l-equiv)
                 (vl-propportlist-equiv (nthcdr acl2::n acl2::l)
                                        (nthcdr acl2::n l-equiv)))
        :rule-classes (:congruence))

Theorem: vl-propportlist-equiv-implies-vl-propportlist-equiv-take-2

(defthm vl-propportlist-equiv-implies-vl-propportlist-equiv-take-2
        (implies (vl-propportlist-equiv acl2::l l-equiv)
                 (vl-propportlist-equiv (take acl2::n acl2::l)
                                        (take acl2::n l-equiv)))
        :rule-classes (:congruence))