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Te-args

Te-args-fix

Fixing function for te-args structures.

Signature
(te-args-fix x) → new-x
Arguments: x — Guard (te-args-p x).
Returns: new-x — Type (te-args-p new-x).

Definitions and Theorems

Function: te-args-fix$inline

(defun te-args-fix$inline (x)
 (declare (xargs :guard (te-args-p x)))
 (let ((acl2::__function__ 'te-args-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (b*
    ((expr-lst (pseudo-term-list-fix (cdr (std::da-nth 0 x))))
     (fn-lst (func-alist-fix (cdr (std::da-nth 1 x))))
     (fty-info (fty-info-alist-fix (cdr (std::da-nth 2 x))))
     (symbol-index (nfix (cdr (std::da-nth 3 x))))
     (symbol-list (str::string-list-fix (cdr (std::da-nth 4 x))))
     (avoid-list (symbol-list-fix (cdr (std::da-nth 5 x))))
     (symbol-map (symbol-string-alist-fix (cdr (std::da-nth 6 x)))))
    (list (cons 'expr-lst expr-lst)
          (cons 'fn-lst fn-lst)
          (cons 'fty-info fty-info)
          (cons 'symbol-index symbol-index)
          (cons 'symbol-list symbol-list)
          (cons 'avoid-list avoid-list)
          (cons 'symbol-map symbol-map)))
   :exec x)))

Theorem: te-args-p-of-te-args-fix

(defthm te-args-p-of-te-args-fix
  (b* ((new-x (te-args-fix$inline x)))
    (te-args-p new-x))
  :rule-classes :rewrite)

Theorem: te-args-fix-when-te-args-p

(defthm te-args-fix-when-te-args-p
  (implies (te-args-p x)
           (equal (te-args-fix x) x)))

Function: te-args-equiv$inline

(defun te-args-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (te-args-p acl2::x)
                              (te-args-p acl2::y))))
  (equal (te-args-fix acl2::x)
         (te-args-fix acl2::y)))

Theorem: te-args-equiv-is-an-equivalence

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

Theorem: te-args-equiv-implies-equal-te-args-fix-1

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

Theorem: te-args-fix-under-te-args-equiv

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

Theorem: equal-of-te-args-fix-1-forward-to-te-args-equiv

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

Theorem: equal-of-te-args-fix-2-forward-to-te-args-equiv

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

Theorem: te-args-equiv-of-te-args-fix-1-forward

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

Theorem: te-args-equiv-of-te-args-fix-2-forward

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