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Integer-literal

Integer-literal-fix

Fixing function for integer-literal structures.

Signature
(integer-literal-fix x) → new-x
Arguments: x — Guard (integer-literalp x).
Returns: new-x — Type (integer-literalp new-x).

Definitions and Theorems

Function: integer-literal-fix$inline

(defun integer-literal-fix$inline (x)
 (declare (xargs :guard (integer-literalp x)))
 (let ((__function__ 'integer-literal-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (integer-literal-kind x)
    (:hex
       (b* ((get (hex-integer-literal-fix (std::da-nth 0 (cdr x)))))
         (cons :hex (list get))))
    (:dec
       (b* ((get (dec-integer-literal-fix (std::da-nth 0 (cdr x)))))
         (cons :dec (list get))))
    (:oct
       (b* ((get (oct-integer-literal-fix (std::da-nth 0 (cdr x)))))
         (cons :oct (list get))))
    (:bin
       (b* ((get (bin-integer-literal-fix (std::da-nth 0 (cdr x)))))
         (cons :bin (list get)))))
   :exec x)))

Theorem: integer-literalp-of-integer-literal-fix

(defthm integer-literalp-of-integer-literal-fix
  (b* ((new-x (integer-literal-fix$inline x)))
    (integer-literalp new-x))
  :rule-classes :rewrite)

Theorem: integer-literal-fix-when-integer-literalp

(defthm integer-literal-fix-when-integer-literalp
  (implies (integer-literalp x)
           (equal (integer-literal-fix x) x)))

Function: integer-literal-equiv$inline

(defun integer-literal-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (integer-literalp acl2::x)
                              (integer-literalp acl2::y))))
  (equal (integer-literal-fix acl2::x)
         (integer-literal-fix acl2::y)))

Theorem: integer-literal-equiv-is-an-equivalence

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

Theorem: integer-literal-equiv-implies-equal-integer-literal-fix-1

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

Theorem: integer-literal-fix-under-integer-literal-equiv

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

Theorem: equal-of-integer-literal-fix-1-forward-to-integer-literal-equiv

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

Theorem: equal-of-integer-literal-fix-2-forward-to-integer-literal-equiv

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

Theorem: integer-literal-equiv-of-integer-literal-fix-1-forward

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

Theorem: integer-literal-equiv-of-integer-literal-fix-2-forward

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

Theorem: integer-literal-kind$inline-of-integer-literal-fix-x

(defthm integer-literal-kind$inline-of-integer-literal-fix-x
  (equal (integer-literal-kind$inline (integer-literal-fix x))
         (integer-literal-kind$inline x)))

Theorem: integer-literal-kind$inline-integer-literal-equiv-congruence-on-x

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

Theorem: consp-of-integer-literal-fix

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