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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)