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• Integral-value

Integral-value-fix

Fixing function for integral-value structures.

Signature

(integral-value-fix acl2::x) → new-x

Arguments

acl2::x — Guard (integral-valuep acl2::x).

Returns

new-x — Type (integral-valuep new-x).

Definitions and Theorems

Function: integral-value-fix$inline

(defun integral-value-fix$inline (acl2::x)
  (declare (xargs :guard (integral-valuep acl2::x)))
  (let ((__function__ 'integral-value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (integral-value-kind acl2::x)
           (:char (b* ((get (char-value-fix acl2::x)))
                    get))
           (:byte (b* ((get (byte-value-fix acl2::x)))
                    get))
           (:short (b* ((get (short-value-fix acl2::x)))
                     get))
           (:int (b* ((get (int-value-fix acl2::x)))
                   get))
           (:long (b* ((get (long-value-fix acl2::x)))
                    get)))
         :exec acl2::x)))

Theorem: integral-valuep-of-integral-value-fix

(defthm integral-valuep-of-integral-value-fix
  (b* ((new-x (integral-value-fix$inline acl2::x)))
    (integral-valuep new-x))
  :rule-classes :rewrite)

Theorem: integral-value-fix-when-integral-valuep

(defthm integral-value-fix-when-integral-valuep
  (implies (integral-valuep acl2::x)
           (equal (integral-value-fix acl2::x)
                  acl2::x)))

Function: integral-value-equiv$inline

(defun integral-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (integral-valuep acl2::x)
                              (integral-valuep acl2::y))))
  (equal (integral-value-fix acl2::x)
         (integral-value-fix acl2::y)))

Theorem: integral-value-equiv-is-an-equivalence

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

Theorem: integral-value-equiv-implies-equal-integral-value-fix-1

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

Theorem: integral-value-fix-under-integral-value-equiv

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

Theorem: equal-of-integral-value-fix-1-forward-to-integral-value-equiv

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

Theorem: equal-of-integral-value-fix-2-forward-to-integral-value-equiv

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

Theorem: integral-value-equiv-of-integral-value-fix-1-forward

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

Theorem: integral-value-equiv-of-integral-value-fix-2-forward

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

Theorem: integral-value-kind$inline-of-integral-value-fix-x

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

Theorem: integral-value-kind$inline-integral-value-equiv-congruence-on-x

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

Theorem: consp-of-integral-value-fix

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