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Annotation

Annotation-fix

Fixing function for annotation structures.

Signature
(annotation-fix x) → new-x
Arguments: x — Guard (annotationp x).
Returns: new-x — Type (annotationp new-x).

Definitions and Theorems

Function: annotation-fix$inline

(defun annotation-fix$inline (x)
  (declare (xargs :guard (annotationp x)))
  (let ((__function__ 'annotation-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (identifier-fix (cdr (std::da-nth 0 x)))))
           (list (cons 'name name)))
         :exec x)))

Theorem: annotationp-of-annotation-fix

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

Theorem: annotation-fix-when-annotationp

(defthm annotation-fix-when-annotationp
  (implies (annotationp x)
           (equal (annotation-fix x) x)))

Function: annotation-equiv$inline

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

Theorem: annotation-equiv-is-an-equivalence

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

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

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

Theorem: annotation-fix-under-annotation-equiv

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

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

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

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

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

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

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

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

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