		Search-engine friendly clone of the ACL2 documentation.

Pristate

Pristate-fix

Fixing function for pristate structures.

Signature
(pristate-fix x) → new-x
Arguments: x — Guard (pristatep x).
Returns: new-x — Type (pristatep new-x).

Definitions and Theorems

Function: pristate-fix$inline

(defun pristate-fix$inline (x)
  (declare (xargs :guard (pristatep x)))
  (let ((__function__ 'pristate-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((bytes-rev (byte-list-fix (cdr (std::da-nth 0 x))))
              (indent-level (nfix (cdr (std::da-nth 1 x))))
              (options (priopt-fix (cdr (std::da-nth 2 x)))))
           (list (cons 'bytes-rev bytes-rev)
                 (cons 'indent-level indent-level)
                 (cons 'options options)))
         :exec x)))

Theorem: pristatep-of-pristate-fix

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

Theorem: pristate-fix-when-pristatep

(defthm pristate-fix-when-pristatep
  (implies (pristatep x)
           (equal (pristate-fix x) x)))

Function: pristate-equiv$inline

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

Theorem: pristate-equiv-is-an-equivalence

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

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

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

Theorem: pristate-fix-under-pristate-equiv

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

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

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

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

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

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

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

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

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