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State64

State64-fix

Fixing function for state64 structures.

Signature
(state64-fix x) → new-x
Arguments: x — Guard (state64p x).
Returns: new-x — Type (state64p new-x).

Definitions and Theorems

Function: state64-fix$inline

(defun state64-fix$inline (x)
  (declare (xargs :guard (state64p x)))
  (let ((__function__ 'state64-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((xregfile (xregfile64-fix (std::da-nth 0 (cdr x))))
              (pc (ubyte64-fix (std::da-nth 1 (cdr x))))
              (mem (memory64-fix (std::da-nth 2 (cdr x))))
              (error (acl2::bool-fix (std::da-nth 3 (cdr x)))))
           (cons :state64 (list xregfile pc mem error)))
         :exec x)))

Theorem: state64p-of-state64-fix

(defthm state64p-of-state64-fix
  (b* ((new-x (state64-fix$inline x)))
    (state64p new-x))
  :rule-classes :rewrite)

Theorem: state64-fix-when-state64p

(defthm state64-fix-when-state64p
  (implies (state64p x)
           (equal (state64-fix x) x)))

Function: state64-equiv$inline

(defun state64-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (state64p acl2::x)
                              (state64p acl2::y))))
  (equal (state64-fix acl2::x)
         (state64-fix acl2::y)))

Theorem: state64-equiv-is-an-equivalence

(defthm state64-equiv-is-an-equivalence
  (and (booleanp (state64-equiv x y))
       (state64-equiv x x)
       (implies (state64-equiv x y)
                (state64-equiv y x))
       (implies (and (state64-equiv x y)
                     (state64-equiv y z))
                (state64-equiv x z)))
  :rule-classes (:equivalence))

Theorem: state64-equiv-implies-equal-state64-fix-1

(defthm state64-equiv-implies-equal-state64-fix-1
  (implies (state64-equiv acl2::x x-equiv)
           (equal (state64-fix acl2::x)
                  (state64-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: state64-fix-under-state64-equiv

(defthm state64-fix-under-state64-equiv
  (state64-equiv (state64-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-state64-fix-1-forward-to-state64-equiv

(defthm equal-of-state64-fix-1-forward-to-state64-equiv
  (implies (equal (state64-fix acl2::x) acl2::y)
           (state64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-state64-fix-2-forward-to-state64-equiv

(defthm equal-of-state64-fix-2-forward-to-state64-equiv
  (implies (equal acl2::x (state64-fix acl2::y))
           (state64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: state64-equiv-of-state64-fix-1-forward

(defthm state64-equiv-of-state64-fix-1-forward
  (implies (state64-equiv (state64-fix acl2::x)
                          acl2::y)
           (state64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: state64-equiv-of-state64-fix-2-forward

(defthm state64-equiv-of-state64-fix-2-forward
  (implies (state64-equiv acl2::x (state64-fix acl2::y))
           (state64-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)