Fixing function for atj-test-value structures.
(atj-test-value-fix x) → new-x
Function:
(defun atj-test-value-fix$inline (x) (declare (xargs :guard (atj-test-valuep x))) (let ((__function__ 'atj-test-value-fix)) (declare (ignorable __function__)) (mbe :logic (case (atj-test-value-kind x) (:acl2 (b* ((get (identity (std::da-nth 0 (cdr x))))) (cons :acl2 (list get)))) (:jboolean (b* ((get (boolean-value-fix (std::da-nth 0 (cdr x))))) (cons :jboolean (list get)))) (:jchar (b* ((get (char-value-fix (std::da-nth 0 (cdr x))))) (cons :jchar (list get)))) (:jbyte (b* ((get (byte-value-fix (std::da-nth 0 (cdr x))))) (cons :jbyte (list get)))) (:jshort (b* ((get (short-value-fix (std::da-nth 0 (cdr x))))) (cons :jshort (list get)))) (:jint (b* ((get (int-value-fix (std::da-nth 0 (cdr x))))) (cons :jint (list get)))) (:jlong (b* ((get (long-value-fix (std::da-nth 0 (cdr x))))) (cons :jlong (list get)))) (:jboolean[] (b* ((get (boolean-array-fix (std::da-nth 0 (cdr x))))) (cons :jboolean[] (list get)))) (:jchar[] (b* ((get (char-array-fix (std::da-nth 0 (cdr x))))) (cons :jchar[] (list get)))) (:jbyte[] (b* ((get (byte-array-fix (std::da-nth 0 (cdr x))))) (cons :jbyte[] (list get)))) (:jshort[] (b* ((get (short-array-fix (std::da-nth 0 (cdr x))))) (cons :jshort[] (list get)))) (:jint[] (b* ((get (int-array-fix (std::da-nth 0 (cdr x))))) (cons :jint[] (list get)))) (:jlong[] (b* ((get (long-array-fix (std::da-nth 0 (cdr x))))) (cons :jlong[] (list get))))) :exec x)))
Theorem:
(defthm atj-test-valuep-of-atj-test-value-fix (b* ((new-x (atj-test-value-fix$inline x))) (atj-test-valuep new-x)) :rule-classes :rewrite)
Theorem:
(defthm atj-test-value-fix-when-atj-test-valuep (implies (atj-test-valuep x) (equal (atj-test-value-fix x) x)))
Function:
(defun atj-test-value-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (atj-test-valuep acl2::x) (atj-test-valuep acl2::y)))) (equal (atj-test-value-fix acl2::x) (atj-test-value-fix acl2::y)))
Theorem:
(defthm atj-test-value-equiv-is-an-equivalence (and (booleanp (atj-test-value-equiv x y)) (atj-test-value-equiv x x) (implies (atj-test-value-equiv x y) (atj-test-value-equiv y x)) (implies (and (atj-test-value-equiv x y) (atj-test-value-equiv y z)) (atj-test-value-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm atj-test-value-equiv-implies-equal-atj-test-value-fix-1 (implies (atj-test-value-equiv acl2::x x-equiv) (equal (atj-test-value-fix acl2::x) (atj-test-value-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm atj-test-value-fix-under-atj-test-value-equiv (atj-test-value-equiv (atj-test-value-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-atj-test-value-fix-1-forward-to-atj-test-value-equiv (implies (equal (atj-test-value-fix acl2::x) acl2::y) (atj-test-value-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-atj-test-value-fix-2-forward-to-atj-test-value-equiv (implies (equal acl2::x (atj-test-value-fix acl2::y)) (atj-test-value-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm atj-test-value-equiv-of-atj-test-value-fix-1-forward (implies (atj-test-value-equiv (atj-test-value-fix acl2::x) acl2::y) (atj-test-value-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm atj-test-value-equiv-of-atj-test-value-fix-2-forward (implies (atj-test-value-equiv acl2::x (atj-test-value-fix acl2::y)) (atj-test-value-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm atj-test-value-kind$inline-of-atj-test-value-fix-x (equal (atj-test-value-kind$inline (atj-test-value-fix x)) (atj-test-value-kind$inline x)))
Theorem:
(defthm atj-test-value-kind$inline-atj-test-value-equiv-congruence-on-x (implies (atj-test-value-equiv x x-equiv) (equal (atj-test-value-kind$inline x) (atj-test-value-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-atj-test-value-fix (consp (atj-test-value-fix x)) :rule-classes :type-prescription)