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Cinteger

Cinteger-fix

Fixing function for cinteger structures.

Signature
(cinteger-fix acl2::x) → new-x
Arguments: acl2::x — Guard (cintegerp acl2::x).
Returns: new-x — Type (cintegerp new-x).

Definitions and Theorems

Function: cinteger-fix$inline

(defun cinteger-fix$inline (acl2::x)
  (declare (xargs :guard (cintegerp acl2::x)))
  (let ((__function__ 'cinteger-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (cinteger-kind acl2::x)
           (:schar (b* ((get (schar-fix acl2::x))) get))
           (:uchar (b* ((get (uchar-fix acl2::x))) get))
           (:sshort (b* ((get (sshort-fix acl2::x))) get))
           (:ushort (b* ((get (ushort-fix acl2::x))) get))
           (:sint (b* ((get (sint-fix acl2::x))) get))
           (:uint (b* ((get (uint-fix acl2::x))) get))
           (:slong (b* ((get (slong-fix acl2::x))) get))
           (:ulong (b* ((get (ulong-fix acl2::x))) get))
           (:sllong (b* ((get (sllong-fix acl2::x))) get))
           (:ullong (b* ((get (ullong-fix acl2::x))) get)))
         :exec acl2::x)))

Theorem: cintegerp-of-cinteger-fix

(defthm cintegerp-of-cinteger-fix
  (b* ((new-x (cinteger-fix$inline acl2::x)))
    (cintegerp new-x))
  :rule-classes :rewrite)

Theorem: cinteger-fix-when-cintegerp

(defthm cinteger-fix-when-cintegerp
  (implies (cintegerp acl2::x)
           (equal (cinteger-fix acl2::x) acl2::x)))

Function: cinteger-equiv$inline

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

Theorem: cinteger-equiv-is-an-equivalence

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

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

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

Theorem: cinteger-fix-under-cinteger-equiv

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

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

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

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

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

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

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

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

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

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

(defthm cinteger-kind$inline-of-cinteger-fix-x
  (equal (cinteger-kind$inline (cinteger-fix acl2::x))
         (cinteger-kind$inline acl2::x)))

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

(defthm cinteger-kind$inline-cinteger-equiv-congruence-on-x
  (implies (cinteger-equiv acl2::x x-equiv)
           (equal (cinteger-kind$inline acl2::x)
                  (cinteger-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-cinteger-fix

(defthm consp-of-cinteger-fix
  (consp (cinteger-fix acl2::x))
  :rule-classes :type-prescription)