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Exception-desc-p

Signature
(exception-desc-p x) → *

Definitions and Theorems

Function: exception-desc-p

(defun exception-desc-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'exception-desc-p))
    (declare (ignorable __function__))
    (and (alistp x)
         (subsetp-equal (strip-cars x)
                        '(:ex :ud :gp :nm)))))

Function: exception-desc-fix

(defun exception-desc-fix (x)
  (declare (xargs :guard (exception-desc-p x)))
  (let ((__function__ 'exception-desc-fix))
    (declare (ignorable __function__))
    (mbe :logic (if (exception-desc-p x) x 'nil)
         :exec x)))

Function: exception-desc-equiv$inline

(defun exception-desc-equiv$inline (x y)
  (declare (xargs :guard (and (exception-desc-p x)
                              (exception-desc-p y))))
  (equal (exception-desc-fix x)
         (exception-desc-fix y)))

Theorem: exception-desc-equiv-is-an-equivalence

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

Theorem: exception-desc-equiv-implies-equal-exception-desc-fix-1

(defthm exception-desc-equiv-implies-equal-exception-desc-fix-1
  (implies (exception-desc-equiv x x-equiv)
           (equal (exception-desc-fix x)
                  (exception-desc-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: exception-desc-fix-under-exception-desc-equiv

(defthm exception-desc-fix-under-exception-desc-equiv
  (exception-desc-equiv (exception-desc-fix x)
                        x)
  :rule-classes (:rewrite :rewrite-quoted-constant))