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Atj-test

Atj-test-fix

Fixing function for atj-test structures.

Signature
(atj-test-fix x) → new-x
Arguments: x — Guard (atj-testp x).
Returns: new-x — Type (atj-testp new-x).

Definitions and Theorems

Function: atj-test-fix$inline

(defun atj-test-fix$inline (x)
 (declare (xargs :guard (atj-testp x)))
 (let ((__function__ 'atj-test-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b* ((name (str-fix (cdr (std::da-nth 0 x))))
        (function (acl2::symbol-fix (cdr (std::da-nth 1 x))))
        (inputs (atj-test-value-list-fix (cdr (std::da-nth 2 x))))
        (outputs (atj-test-value-list-fix (cdr (std::da-nth 3 x)))))
     (list (cons 'name name)
           (cons 'function function)
           (cons 'inputs inputs)
           (cons 'outputs outputs)))
   :exec x)))

Theorem: atj-testp-of-atj-test-fix

(defthm atj-testp-of-atj-test-fix
  (b* ((new-x (atj-test-fix$inline x)))
    (atj-testp new-x))
  :rule-classes :rewrite)

Theorem: atj-test-fix-when-atj-testp

(defthm atj-test-fix-when-atj-testp
  (implies (atj-testp x)
           (equal (atj-test-fix x) x)))

Function: atj-test-equiv$inline

(defun atj-test-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (atj-testp acl2::x)
                              (atj-testp acl2::y))))
  (equal (atj-test-fix acl2::x)
         (atj-test-fix acl2::y)))

Theorem: atj-test-equiv-is-an-equivalence

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

Theorem: atj-test-equiv-implies-equal-atj-test-fix-1

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

Theorem: atj-test-fix-under-atj-test-equiv

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

Theorem: equal-of-atj-test-fix-1-forward-to-atj-test-equiv

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

Theorem: equal-of-atj-test-fix-2-forward-to-atj-test-equiv

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

Theorem: atj-test-equiv-of-atj-test-fix-1-forward

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

Theorem: atj-test-equiv-of-atj-test-fix-2-forward

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