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Chars+exprs

Chars+exprs-fix

Fixing function for chars+exprs structures.

Signature
(chars+exprs-fix x) → new-x
Arguments: x — Guard (chars+exprs-p x).
Returns: new-x — Type (chars+exprs-p new-x).

Definitions and Theorems

Function: chars+exprs-fix$inline

(defun chars+exprs-fix$inline (x)
 (declare (xargs :guard (chars+exprs-p x)))
 (let ((__function__ 'chars+exprs-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((chars (char-list-fix (cdr (std::da-nth 0 (cdr x)))))
        (exprs (expression-list-fix (cdr (std::da-nth 1 (cdr x))))))
     (cons :chars+exprs (list (cons 'chars chars)
                              (cons 'exprs exprs))))
   :exec x)))

Theorem: chars+exprs-p-of-chars+exprs-fix

(defthm chars+exprs-p-of-chars+exprs-fix
  (b* ((new-x (chars+exprs-fix$inline x)))
    (chars+exprs-p new-x))
  :rule-classes :rewrite)

Theorem: chars+exprs-fix-when-chars+exprs-p

(defthm chars+exprs-fix-when-chars+exprs-p
  (implies (chars+exprs-p x)
           (equal (chars+exprs-fix x) x)))

Function: chars+exprs-equiv$inline

(defun chars+exprs-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (chars+exprs-p acl2::x)
                              (chars+exprs-p acl2::y))))
  (equal (chars+exprs-fix acl2::x)
         (chars+exprs-fix acl2::y)))

Theorem: chars+exprs-equiv-is-an-equivalence

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

Theorem: chars+exprs-equiv-implies-equal-chars+exprs-fix-1

(defthm chars+exprs-equiv-implies-equal-chars+exprs-fix-1
  (implies (chars+exprs-equiv acl2::x x-equiv)
           (equal (chars+exprs-fix acl2::x)
                  (chars+exprs-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: chars+exprs-fix-under-chars+exprs-equiv

(defthm chars+exprs-fix-under-chars+exprs-equiv
  (chars+exprs-equiv (chars+exprs-fix acl2::x)
                     acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-chars+exprs-fix-1-forward-to-chars+exprs-equiv

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

Theorem: equal-of-chars+exprs-fix-2-forward-to-chars+exprs-equiv

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

Theorem: chars+exprs-equiv-of-chars+exprs-fix-1-forward

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

Theorem: chars+exprs-equiv-of-chars+exprs-fix-2-forward

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