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Junop

Junop-fix

Fixing function for junop structures.

Signature
(junop-fix x) → new-x
Arguments: x — Guard (junopp x).
Returns: new-x — Type (junopp new-x).

Definitions and Theorems

Function: junop-fix$inline

(defun junop-fix$inline (x)
  (declare (xargs :guard (junopp x)))
  (let ((__function__ 'junop-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (junop-kind x)
           (:preinc (cons :preinc (list)))
           (:predec (cons :predec (list)))
           (:uplus (cons :uplus (list)))
           (:uminus (cons :uminus (list)))
           (:bitcompl (cons :bitcompl (list)))
           (:logcompl (cons :logcompl (list))))
         :exec x)))

Theorem: junopp-of-junop-fix

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

Theorem: junop-fix-when-junopp

(defthm junop-fix-when-junopp
  (implies (junopp x)
           (equal (junop-fix x) x)))

Function: junop-equiv$inline

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

Theorem: junop-equiv-is-an-equivalence

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

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

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

Theorem: junop-fix-under-junop-equiv

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

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

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

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

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

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

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

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

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

Theorem: junop-kind$inline-of-junop-fix-x

(defthm junop-kind$inline-of-junop-fix-x
  (equal (junop-kind$inline (junop-fix x))
         (junop-kind$inline x)))

Theorem: junop-kind$inline-junop-equiv-congruence-on-x

(defthm junop-kind$inline-junop-equiv-congruence-on-x
  (implies (junop-equiv x x-equiv)
           (equal (junop-kind$inline x)
                  (junop-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-junop-fix

(defthm consp-of-junop-fix
  (consp (junop-fix x))
  :rule-classes :type-prescription)