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Svstack

Svstack-fix

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

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

In the logic, we apply svex-alist-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: svstack-fix$inline

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

Theorem: svstack-p-of-svstack-fix

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

Theorem: svstack-fix-when-svstack-p

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

Function: svstack-equiv$inline

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

Theorem: svstack-equiv-is-an-equivalence

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

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

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

Theorem: svstack-fix-under-svstack-equiv

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

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

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

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

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

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

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

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

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

Theorem: car-of-svstack-fix-x-under-svex-alist-equiv

(defthm car-of-svstack-fix-x-under-svex-alist-equiv
  (svex-alist-equiv (car (svstack-fix x))
                    (car x)))

Theorem: car-svstack-equiv-congruence-on-x-under-svex-alist-equiv

(defthm car-svstack-equiv-congruence-on-x-under-svex-alist-equiv
  (implies (svstack-equiv x x-equiv)
           (svex-alist-equiv (car x)
                             (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-svstack-fix-x-under-svstack-equiv

(defthm cdr-of-svstack-fix-x-under-svstack-equiv
  (svstack-equiv (cdr (svstack-fix x))
                 (cdr x)))

Theorem: cdr-svstack-equiv-congruence-on-x-under-svstack-equiv

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

Theorem: cons-of-svex-alist-fix-x-under-svstack-equiv

(defthm cons-of-svex-alist-fix-x-under-svstack-equiv
  (svstack-equiv (cons (svex-alist-fix x) y)
                 (cons x y)))

Theorem: cons-svex-alist-equiv-congruence-on-x-under-svstack-equiv

(defthm cons-svex-alist-equiv-congruence-on-x-under-svstack-equiv
  (implies (svex-alist-equiv x x-equiv)
           (svstack-equiv (cons x y)
                          (cons x-equiv y)))
  :rule-classes :congruence)

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

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

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

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

Theorem: consp-of-svstack-fix

(defthm consp-of-svstack-fix
  (equal (consp (svstack-fix x))
         (consp x)))

Theorem: svstack-fix-of-cons

(defthm svstack-fix-of-cons
  (equal (svstack-fix (cons a x))
         (cons (svex-alist-fix a)
               (svstack-fix x))))

Theorem: len-of-svstack-fix

(defthm len-of-svstack-fix
  (equal (len (svstack-fix x)) (len x)))

Theorem: svstack-fix-of-append

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

Theorem: svstack-fix-of-repeat

(defthm svstack-fix-of-repeat
  (equal (svstack-fix (repeat acl2::n x))
         (repeat acl2::n (svex-alist-fix x))))

Theorem: nth-of-svstack-fix

(defthm nth-of-svstack-fix
  (equal (nth acl2::n (svstack-fix x))
         (if (< (nfix acl2::n) (len x))
             (svex-alist-fix (nth acl2::n x))
           nil)))

Theorem: svstack-equiv-implies-svstack-equiv-append-1

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

Theorem: svstack-equiv-implies-svstack-equiv-append-2

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

Theorem: svstack-equiv-implies-svstack-equiv-nthcdr-2

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

Theorem: svstack-equiv-implies-svstack-equiv-take-2

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