		Search-engine friendly clone of the ACL2 documentation.

Address-option

Address-option-fix

Fixing function for address-option structures.

Signature
(address-option-fix x) → new-x
Arguments: x — Guard (address-optionp x).
Returns: new-x — Type (address-optionp new-x).

Definitions and Theorems

Function: address-option-fix$inline

(defun address-option-fix$inline (x)
  (declare (xargs :guard (address-optionp x)))
  (let ((__function__ 'address-option-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (address-fix x)))
                           fty::val)))
         :exec x)))

Theorem: address-optionp-of-address-option-fix

(defthm address-optionp-of-address-option-fix
  (b* ((new-x (address-option-fix$inline x)))
    (address-optionp new-x))
  :rule-classes :rewrite)

Theorem: address-option-fix-when-address-optionp

(defthm address-option-fix-when-address-optionp
  (implies (address-optionp x)
           (equal (address-option-fix x) x)))

Function: address-option-equiv$inline

(defun address-option-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (address-optionp acl2::x)
                              (address-optionp acl2::y))))
  (equal (address-option-fix acl2::x)
         (address-option-fix acl2::y)))

Theorem: address-option-equiv-is-an-equivalence

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

Theorem: address-option-equiv-implies-equal-address-option-fix-1

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

Theorem: address-option-fix-under-address-option-equiv

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

Theorem: equal-of-address-option-fix-1-forward-to-address-option-equiv

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

Theorem: equal-of-address-option-fix-2-forward-to-address-option-equiv

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

Theorem: address-option-equiv-of-address-option-fix-1-forward

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

Theorem: address-option-equiv-of-address-option-fix-2-forward

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