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Vcd-wirelist

Vcd-wirelist-fix

(vcd-wirelist-fix x) is a usual fty list fixing function.

Signature
(vcd-wirelist-fix x) → fty::newx
Arguments: x — Guard (vcd-wirelist-p x).
Returns: fty::newx — Type (vcd-wirelist-p fty::newx).

In the logic, we apply vcd-wire-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: vcd-wirelist-fix$inline

(defun vcd-wirelist-fix$inline (x)
  (declare (xargs :guard (vcd-wirelist-p x)))
  (let ((__function__ 'vcd-wirelist-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (vcd-wire-fix (car x))
                 (vcd-wirelist-fix (cdr x))))
         :exec x)))

Theorem: vcd-wirelist-p-of-vcd-wirelist-fix

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

Theorem: vcd-wirelist-fix-when-vcd-wirelist-p

(defthm vcd-wirelist-fix-when-vcd-wirelist-p
  (implies (vcd-wirelist-p x)
           (equal (vcd-wirelist-fix x) x)))

Function: vcd-wirelist-equiv$inline

(defun vcd-wirelist-equiv$inline (x y)
  (declare (xargs :guard (and (vcd-wirelist-p x)
                              (vcd-wirelist-p y))))
  (equal (vcd-wirelist-fix x)
         (vcd-wirelist-fix y)))

Theorem: vcd-wirelist-equiv-is-an-equivalence

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

Theorem: vcd-wirelist-equiv-implies-equal-vcd-wirelist-fix-1

(defthm vcd-wirelist-equiv-implies-equal-vcd-wirelist-fix-1
  (implies (vcd-wirelist-equiv x x-equiv)
           (equal (vcd-wirelist-fix x)
                  (vcd-wirelist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vcd-wirelist-fix-under-vcd-wirelist-equiv

(defthm vcd-wirelist-fix-under-vcd-wirelist-equiv
  (vcd-wirelist-equiv (vcd-wirelist-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vcd-wirelist-fix-1-forward-to-vcd-wirelist-equiv

(defthm equal-of-vcd-wirelist-fix-1-forward-to-vcd-wirelist-equiv
  (implies (equal (vcd-wirelist-fix x) y)
           (vcd-wirelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-vcd-wirelist-fix-2-forward-to-vcd-wirelist-equiv

(defthm equal-of-vcd-wirelist-fix-2-forward-to-vcd-wirelist-equiv
  (implies (equal x (vcd-wirelist-fix y))
           (vcd-wirelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: vcd-wirelist-equiv-of-vcd-wirelist-fix-1-forward

(defthm vcd-wirelist-equiv-of-vcd-wirelist-fix-1-forward
  (implies (vcd-wirelist-equiv (vcd-wirelist-fix x)
                               y)
           (vcd-wirelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: vcd-wirelist-equiv-of-vcd-wirelist-fix-2-forward

(defthm vcd-wirelist-equiv-of-vcd-wirelist-fix-2-forward
  (implies (vcd-wirelist-equiv x (vcd-wirelist-fix y))
           (vcd-wirelist-equiv x y))
  :rule-classes :forward-chaining)

Theorem: car-of-vcd-wirelist-fix-x-under-vcd-wire-equiv

(defthm car-of-vcd-wirelist-fix-x-under-vcd-wire-equiv
  (vcd-wire-equiv (car (vcd-wirelist-fix x))
                  (car x)))

Theorem: car-vcd-wirelist-equiv-congruence-on-x-under-vcd-wire-equiv

(defthm car-vcd-wirelist-equiv-congruence-on-x-under-vcd-wire-equiv
  (implies (vcd-wirelist-equiv x x-equiv)
           (vcd-wire-equiv (car x) (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-vcd-wirelist-fix-x-under-vcd-wirelist-equiv

(defthm cdr-of-vcd-wirelist-fix-x-under-vcd-wirelist-equiv
  (vcd-wirelist-equiv (cdr (vcd-wirelist-fix x))
                      (cdr x)))

Theorem: cdr-vcd-wirelist-equiv-congruence-on-x-under-vcd-wirelist-equiv

(defthm
    cdr-vcd-wirelist-equiv-congruence-on-x-under-vcd-wirelist-equiv
  (implies (vcd-wirelist-equiv x x-equiv)
           (vcd-wirelist-equiv (cdr x)
                               (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-vcd-wire-fix-x-under-vcd-wirelist-equiv

(defthm cons-of-vcd-wire-fix-x-under-vcd-wirelist-equiv
  (vcd-wirelist-equiv (cons (vcd-wire-fix x) y)
                      (cons x y)))

Theorem: cons-vcd-wire-equiv-congruence-on-x-under-vcd-wirelist-equiv

(defthm cons-vcd-wire-equiv-congruence-on-x-under-vcd-wirelist-equiv
  (implies (vcd-wire-equiv x x-equiv)
           (vcd-wirelist-equiv (cons x y)
                               (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-vcd-wirelist-fix-y-under-vcd-wirelist-equiv

(defthm cons-of-vcd-wirelist-fix-y-under-vcd-wirelist-equiv
  (vcd-wirelist-equiv (cons x (vcd-wirelist-fix y))
                      (cons x y)))

Theorem: cons-vcd-wirelist-equiv-congruence-on-y-under-vcd-wirelist-equiv

(defthm
   cons-vcd-wirelist-equiv-congruence-on-y-under-vcd-wirelist-equiv
  (implies (vcd-wirelist-equiv y y-equiv)
           (vcd-wirelist-equiv (cons x y)
                               (cons x y-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-vcd-wirelist-fix

(defthm consp-of-vcd-wirelist-fix
  (equal (consp (vcd-wirelist-fix x))
         (consp x)))

Theorem: vcd-wirelist-fix-under-iff

(defthm vcd-wirelist-fix-under-iff
  (iff (vcd-wirelist-fix x) (consp x)))

Theorem: vcd-wirelist-fix-of-cons

(defthm vcd-wirelist-fix-of-cons
  (equal (vcd-wirelist-fix (cons a x))
         (cons (vcd-wire-fix a)
               (vcd-wirelist-fix x))))

Theorem: len-of-vcd-wirelist-fix

(defthm len-of-vcd-wirelist-fix
  (equal (len (vcd-wirelist-fix x))
         (len x)))

Theorem: vcd-wirelist-fix-of-append

(defthm vcd-wirelist-fix-of-append
  (equal (vcd-wirelist-fix (append std::a std::b))
         (append (vcd-wirelist-fix std::a)
                 (vcd-wirelist-fix std::b))))

Theorem: vcd-wirelist-fix-of-repeat

(defthm vcd-wirelist-fix-of-repeat
  (equal (vcd-wirelist-fix (repeat acl2::n x))
         (repeat acl2::n (vcd-wire-fix x))))

Theorem: list-equiv-refines-vcd-wirelist-equiv

(defthm list-equiv-refines-vcd-wirelist-equiv
  (implies (list-equiv x y)
           (vcd-wirelist-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-vcd-wirelist-fix

(defthm nth-of-vcd-wirelist-fix
  (equal (nth acl2::n (vcd-wirelist-fix x))
         (if (< (nfix acl2::n) (len x))
             (vcd-wire-fix (nth acl2::n x))
           nil)))

Theorem: vcd-wirelist-equiv-implies-vcd-wirelist-equiv-append-1

(defthm vcd-wirelist-equiv-implies-vcd-wirelist-equiv-append-1
  (implies (vcd-wirelist-equiv x fty::x-equiv)
           (vcd-wirelist-equiv (append x y)
                               (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: vcd-wirelist-equiv-implies-vcd-wirelist-equiv-append-2

(defthm vcd-wirelist-equiv-implies-vcd-wirelist-equiv-append-2
  (implies (vcd-wirelist-equiv y fty::y-equiv)
           (vcd-wirelist-equiv (append x y)
                               (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: vcd-wirelist-equiv-implies-vcd-wirelist-equiv-nthcdr-2

(defthm vcd-wirelist-equiv-implies-vcd-wirelist-equiv-nthcdr-2
  (implies (vcd-wirelist-equiv acl2::l l-equiv)
           (vcd-wirelist-equiv (nthcdr acl2::n acl2::l)
                               (nthcdr acl2::n l-equiv)))
  :rule-classes (:congruence))

Theorem: vcd-wirelist-equiv-implies-vcd-wirelist-equiv-take-2

(defthm vcd-wirelist-equiv-implies-vcd-wirelist-equiv-take-2
  (implies (vcd-wirelist-equiv acl2::l l-equiv)
           (vcd-wirelist-equiv (take acl2::n acl2::l)
                               (take acl2::n l-equiv)))
  :rule-classes (:congruence))