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• Vl-function-specialization-map

Vl-function-specialization-map-fix

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

Signature

(vl-function-specialization-map-fix x) → fty::newx

Arguments

x — Guard (vl-function-specialization-map-p x).

Returns

fty::newx — Type (vl-function-specialization-map-p fty::newx).

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

Definitions and Theorems

Function: vl-function-specialization-map-fix$inline

(defun vl-function-specialization-map-fix$inline (x)
 (declare (xargs :guard (vl-function-specialization-map-p x)))
 (let ((__function__ 'vl-function-specialization-map-fix))
   (declare (ignorable __function__))
   (mbe :logic
        (if (atom x)
            nil
          (if (consp (car x))
              (cons (cons (sv::maybe-4veclist-fix (caar x))
                          (vl-function-specialization-fix (cdar x)))
                    (vl-function-specialization-map-fix (cdr x)))
            (vl-function-specialization-map-fix (cdr x))))
        :exec x)))

Theorem: vl-function-specialization-map-p-of-vl-function-specialization-map-fix

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

Theorem: vl-function-specialization-map-fix-when-vl-function-specialization-map-p

(defthm
 vl-function-specialization-map-fix-when-vl-function-specialization-map-p
 (implies (vl-function-specialization-map-p x)
          (equal (vl-function-specialization-map-fix x)
                 x)))

Function: vl-function-specialization-map-equiv$inline

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

Theorem: vl-function-specialization-map-equiv-is-an-equivalence

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

Theorem: vl-function-specialization-map-equiv-implies-equal-vl-function-specialization-map-fix-1

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

Theorem: vl-function-specialization-map-fix-under-vl-function-specialization-map-equiv

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

Theorem: equal-of-vl-function-specialization-map-fix-1-forward-to-vl-function-specialization-map-equiv

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

Theorem: equal-of-vl-function-specialization-map-fix-2-forward-to-vl-function-specialization-map-equiv

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

Theorem: vl-function-specialization-map-equiv-of-vl-function-specialization-map-fix-1-forward

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

Theorem: vl-function-specialization-map-equiv-of-vl-function-specialization-map-fix-2-forward

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

Theorem: cons-of-maybe-4veclist-fix-k-under-vl-function-specialization-map-equiv

(defthm
 cons-of-maybe-4veclist-fix-k-under-vl-function-specialization-map-equiv
 (vl-function-specialization-map-equiv
      (cons (cons (sv::maybe-4veclist-fix acl2::k)
                  acl2::v)
            acl2::x)
      (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-maybe-4veclist-equiv-congruence-on-k-under-vl-function-specialization-map-equiv

(defthm
 cons-maybe-4veclist-equiv-congruence-on-k-under-vl-function-specialization-map-equiv
 (implies (sv::maybe-4veclist-equiv acl2::k k-equiv)
          (vl-function-specialization-map-equiv
               (cons (cons acl2::k acl2::v) acl2::x)
               (cons (cons k-equiv acl2::v) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-vl-function-specialization-fix-v-under-vl-function-specialization-map-equiv

(defthm
 cons-of-vl-function-specialization-fix-v-under-vl-function-specialization-map-equiv
 (vl-function-specialization-map-equiv
      (cons (cons acl2::k
                  (vl-function-specialization-fix acl2::v))
            acl2::x)
      (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-vl-function-specialization-equiv-congruence-on-v-under-vl-function-specialization-map-equiv

(defthm
 cons-vl-function-specialization-equiv-congruence-on-v-under-vl-function-specialization-map-equiv
 (implies (vl-function-specialization-equiv acl2::v v-equiv)
          (vl-function-specialization-map-equiv
               (cons (cons acl2::k acl2::v) acl2::x)
               (cons (cons acl2::k v-equiv) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-vl-function-specialization-map-fix-y-under-vl-function-specialization-map-equiv

(defthm
 cons-of-vl-function-specialization-map-fix-y-under-vl-function-specialization-map-equiv
 (vl-function-specialization-map-equiv
      (cons acl2::x
            (vl-function-specialization-map-fix acl2::y))
      (cons acl2::x acl2::y)))

Theorem: cons-vl-function-specialization-map-equiv-congruence-on-y-under-vl-function-specialization-map-equiv

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

Theorem: vl-function-specialization-map-fix-of-acons

(defthm vl-function-specialization-map-fix-of-acons
  (equal (vl-function-specialization-map-fix
              (cons (cons acl2::a acl2::b) x))
         (cons (cons (sv::maybe-4veclist-fix acl2::a)
                     (vl-function-specialization-fix acl2::b))
               (vl-function-specialization-map-fix x))))

Theorem: vl-function-specialization-map-fix-of-append

(defthm vl-function-specialization-map-fix-of-append
  (equal (vl-function-specialization-map-fix (append std::a std::b))
         (append (vl-function-specialization-map-fix std::a)
                 (vl-function-specialization-map-fix std::b))))

Theorem: consp-car-of-vl-function-specialization-map-fix

(defthm consp-car-of-vl-function-specialization-map-fix
  (equal (consp (car (vl-function-specialization-map-fix x)))
         (consp (vl-function-specialization-map-fix x))))