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Stat32

Stat32-fix

Fixing function for stat32 structures.

Signature
(stat32-fix x) → new-x
Arguments: x — Guard (stat32p x).
Returns: new-x — Type (stat32p new-x).

Definitions and Theorems

Function: stat32-fix$inline

(defun stat32-fix$inline (x)
  (declare (xargs :guard (stat32p x)))
  (mbe :logic
       (b* ((xregs (xregs-fix (cdr (std::da-nth 0 x))))
            (pc (ubyte32-fix (cdr (std::da-nth 1 x))))
            (memory (memory-fix (cdr (std::da-nth 2 x))))
            (error (acl2::bool-fix (cdr (std::da-nth 3 x)))))
         (list (cons 'xregs xregs)
               (cons 'pc pc)
               (cons 'memory memory)
               (cons 'error error)))
       :exec x))

Theorem: stat32p-of-stat32-fix

(defthm stat32p-of-stat32-fix
  (b* ((new-x (stat32-fix$inline x)))
    (stat32p new-x))
  :rule-classes :rewrite)

Theorem: stat32-fix-when-stat32p

(defthm stat32-fix-when-stat32p
  (implies (stat32p x)
           (equal (stat32-fix x) x)))

Function: stat32-equiv$inline

(defun stat32-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (stat32p acl2::x)
                              (stat32p acl2::y))))
  (equal (stat32-fix acl2::x)
         (stat32-fix acl2::y)))

Theorem: stat32-equiv-is-an-equivalence

(defthm stat32-equiv-is-an-equivalence
  (and (booleanp (stat32-equiv x y))
       (stat32-equiv x x)
       (implies (stat32-equiv x y)
                (stat32-equiv y x))
       (implies (and (stat32-equiv x y)
                     (stat32-equiv y z))
                (stat32-equiv x z)))
  :rule-classes (:equivalence))

Theorem: stat32-equiv-implies-equal-stat32-fix-1

(defthm stat32-equiv-implies-equal-stat32-fix-1
  (implies (stat32-equiv acl2::x x-equiv)
           (equal (stat32-fix acl2::x)
                  (stat32-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: stat32-fix-under-stat32-equiv

(defthm stat32-fix-under-stat32-equiv
  (stat32-equiv (stat32-fix acl2::x)
                acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-stat32-fix-1-forward-to-stat32-equiv

(defthm equal-of-stat32-fix-1-forward-to-stat32-equiv
  (implies (equal (stat32-fix acl2::x) acl2::y)
           (stat32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-stat32-fix-2-forward-to-stat32-equiv

(defthm equal-of-stat32-fix-2-forward-to-stat32-equiv
  (implies (equal acl2::x (stat32-fix acl2::y))
           (stat32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: stat32-equiv-of-stat32-fix-1-forward

(defthm stat32-equiv-of-stat32-fix-1-forward
  (implies (stat32-equiv (stat32-fix acl2::x)
                         acl2::y)
           (stat32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: stat32-equiv-of-stat32-fix-2-forward

(defthm stat32-equiv-of-stat32-fix-2-forward
  (implies (stat32-equiv acl2::x (stat32-fix acl2::y))
           (stat32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: stat32-fix$inline-of-stat32-fix-x

(defthm stat32-fix$inline-of-stat32-fix-x
  (equal (stat32-fix$inline (stat32-fix x))
         (stat32-fix$inline x)))

Theorem: stat32-fix$inline-stat32-equiv-congruence-on-x

(defthm stat32-fix$inline-stat32-equiv-congruence-on-x
  (implies (stat32-equiv x x-equiv)
           (equal (stat32-fix$inline x)
                  (stat32-fix$inline x-equiv)))
  :rule-classes :congruence)