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State32

State32-fix

Fixing function for state32 structures.

Signature
(state32-fix x) → new-x
Arguments: x — Guard (state32p x).
Returns: new-x — Type (state32p new-x).

Definitions and Theorems

Function: state32-fix$inline

(defun state32-fix$inline (x)
  (declare (xargs :guard (state32p x)))
  (let ((__function__ 'state32-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((xregfile (xregfile32-fix (std::da-nth 0 (cdr x))))
              (pc (ubyte32-fix (std::da-nth 1 (cdr x))))
              (mem (memory32-fix (std::da-nth 2 (cdr x))))
              (error (acl2::bool-fix (std::da-nth 3 (cdr x)))))
           (cons :state32 (list xregfile pc mem error)))
         :exec x)))

Theorem: state32p-of-state32-fix

(defthm state32p-of-state32-fix
  (b* ((new-x (state32-fix$inline x)))
    (state32p new-x))
  :rule-classes :rewrite)

Theorem: state32-fix-when-state32p

(defthm state32-fix-when-state32p
  (implies (state32p x)
           (equal (state32-fix x) x)))

Function: state32-equiv$inline

(defun state32-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (state32p acl2::x)
                              (state32p acl2::y))))
  (equal (state32-fix acl2::x)
         (state32-fix acl2::y)))

Theorem: state32-equiv-is-an-equivalence

(defthm state32-equiv-is-an-equivalence
  (and (booleanp (state32-equiv x y))
       (state32-equiv x x)
       (implies (state32-equiv x y)
                (state32-equiv y x))
       (implies (and (state32-equiv x y)
                     (state32-equiv y z))
                (state32-equiv x z)))
  :rule-classes (:equivalence))

Theorem: state32-equiv-implies-equal-state32-fix-1

(defthm state32-equiv-implies-equal-state32-fix-1
  (implies (state32-equiv acl2::x x-equiv)
           (equal (state32-fix acl2::x)
                  (state32-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: state32-fix-under-state32-equiv

(defthm state32-fix-under-state32-equiv
  (state32-equiv (state32-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-state32-fix-1-forward-to-state32-equiv

(defthm equal-of-state32-fix-1-forward-to-state32-equiv
  (implies (equal (state32-fix acl2::x) acl2::y)
           (state32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-state32-fix-2-forward-to-state32-equiv

(defthm equal-of-state32-fix-2-forward-to-state32-equiv
  (implies (equal acl2::x (state32-fix acl2::y))
           (state32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: state32-equiv-of-state32-fix-1-forward

(defthm state32-equiv-of-state32-fix-1-forward
  (implies (state32-equiv (state32-fix acl2::x)
                          acl2::y)
           (state32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: state32-equiv-of-state32-fix-2-forward

(defthm state32-equiv-of-state32-fix-2-forward
  (implies (state32-equiv acl2::x (state32-fix acl2::y))
           (state32-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)