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Svexl

Svexl-fix

Fixing function for svexl structures.

Signature
(svexl-fix x) → new-x
Arguments: x — Guard (svexl-p x).
Returns: new-x — Type (svexl-p new-x).

Definitions and Theorems

Function: svexl-fix$inline

(defun svexl-fix$inline (x)
 (declare (xargs :guard (svexl-p x)))
 (let ((acl2::__function__ 'svexl-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (b* ((top-node (svexl-node-fix (cdr (std::da-nth 0 x))))
        (node-array (svexl-node-array-fix (cdr (std::da-nth 1 x)))))
     (list (cons 'top-node top-node)
           (cons 'node-array node-array)))
   :exec x)))

Theorem: svexl-p-of-svexl-fix

(defthm svexl-p-of-svexl-fix
  (b* ((new-x (svexl-fix$inline x)))
    (svexl-p new-x))
  :rule-classes :rewrite)

Theorem: svexl-fix-when-svexl-p

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

Function: svexl-equiv$inline

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

Theorem: svexl-equiv-is-an-equivalence

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

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

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

Theorem: svexl-fix-under-svexl-equiv

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

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

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

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

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

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

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

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

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