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Netassigns

Netassigns-fix

(netassigns-fix x) is an fty alist fixing function that follows the fix-keys strategy.

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

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: netassigns-fix$inline

(defun netassigns-fix$inline (x)
  (declare (xargs :guard (netassigns-p x)))
  (let ((__function__ 'netassigns-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             x
           (if (consp (car x))
               (cons (cons (svar-fix (caar x))
                           (driverlist-fix (cdar x)))
                     (netassigns-fix (cdr x)))
             (netassigns-fix (cdr x))))
         :exec x)))

Theorem: netassigns-p-of-netassigns-fix

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

Theorem: netassigns-fix-when-netassigns-p

(defthm netassigns-fix-when-netassigns-p
  (implies (netassigns-p x)
           (equal (netassigns-fix x) x)))

Function: netassigns-equiv$inline

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

Theorem: netassigns-equiv-is-an-equivalence

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

Theorem: netassigns-equiv-implies-equal-netassigns-fix-1

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

Theorem: netassigns-fix-under-netassigns-equiv

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

Theorem: equal-of-netassigns-fix-1-forward-to-netassigns-equiv

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

Theorem: equal-of-netassigns-fix-2-forward-to-netassigns-equiv

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

Theorem: netassigns-equiv-of-netassigns-fix-1-forward

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

Theorem: netassigns-equiv-of-netassigns-fix-2-forward

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

Theorem: cons-of-svar-fix-k-under-netassigns-equiv

(defthm cons-of-svar-fix-k-under-netassigns-equiv
  (netassigns-equiv (cons (cons (svar-fix acl2::k) acl2::v)
                          x)
                    (cons (cons acl2::k acl2::v) x)))

Theorem: cons-svar-equiv-congruence-on-k-under-netassigns-equiv

(defthm cons-svar-equiv-congruence-on-k-under-netassigns-equiv
  (implies (svar-equiv acl2::k k-equiv)
           (netassigns-equiv (cons (cons acl2::k acl2::v) x)
                             (cons (cons k-equiv acl2::v) x)))
  :rule-classes :congruence)

Theorem: cons-of-driverlist-fix-v-under-netassigns-equiv

(defthm cons-of-driverlist-fix-v-under-netassigns-equiv
  (netassigns-equiv (cons (cons acl2::k (driverlist-fix acl2::v))
                          x)
                    (cons (cons acl2::k acl2::v) x)))

Theorem: cons-driverlist-equiv-congruence-on-v-under-netassigns-equiv

(defthm cons-driverlist-equiv-congruence-on-v-under-netassigns-equiv
  (implies (driverlist-equiv acl2::v v-equiv)
           (netassigns-equiv (cons (cons acl2::k acl2::v) x)
                             (cons (cons acl2::k v-equiv) x)))
  :rule-classes :congruence)

Theorem: cons-of-netassigns-fix-y-under-netassigns-equiv

(defthm cons-of-netassigns-fix-y-under-netassigns-equiv
  (netassigns-equiv (cons x (netassigns-fix y))
                    (cons x y)))

Theorem: cons-netassigns-equiv-congruence-on-y-under-netassigns-equiv

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

Theorem: netassigns-fix-of-acons

(defthm netassigns-fix-of-acons
  (equal (netassigns-fix (cons (cons acl2::a acl2::b) x))
         (cons (cons (svar-fix acl2::a)
                     (driverlist-fix acl2::b))
               (netassigns-fix x))))

Theorem: netassigns-fix-of-append

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

Theorem: consp-car-of-netassigns-fix

(defthm consp-car-of-netassigns-fix
  (equal (consp (car (netassigns-fix x)))
         (consp (netassigns-fix x))))