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Isuffix

Isuffix-fix

Fixing function for isuffix structures.

Signature
(isuffix-fix x) → new-x
Arguments: x — Guard (isuffixp x).
Returns: new-x — Type (isuffixp new-x).

Definitions and Theorems

Function: isuffix-fix$inline

(defun isuffix-fix$inline (x)
 (declare (xargs :guard (isuffixp x)))
 (let ((__function__ 'isuffix-fix))
  (declare (ignorable __function__))
  (mbe :logic
       (case (isuffix-kind x)
         (:u (b* ((unsigned (usuffix-fix (std::da-nth 0 (cdr x)))))
               (cons :u (list unsigned))))
         (:l (b* ((length (lsuffix-fix (std::da-nth 0 (cdr x)))))
               (cons :l (list length))))
         (:ul (b* ((unsigned (usuffix-fix (std::da-nth 0 (cdr x))))
                   (length (lsuffix-fix (std::da-nth 1 (cdr x)))))
                (cons :ul (list unsigned length))))
         (:lu (b* ((length (lsuffix-fix (std::da-nth 0 (cdr x))))
                   (unsigned (usuffix-fix (std::da-nth 1 (cdr x)))))
                (cons :lu (list length unsigned)))))
       :exec x)))

Theorem: isuffixp-of-isuffix-fix

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

Theorem: isuffix-fix-when-isuffixp

(defthm isuffix-fix-when-isuffixp
  (implies (isuffixp x)
           (equal (isuffix-fix x) x)))

Function: isuffix-equiv$inline

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

Theorem: isuffix-equiv-is-an-equivalence

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

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

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

Theorem: isuffix-fix-under-isuffix-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-isuffix-fix

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