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Superscripts-p

Signature
(superscripts-p x) → *

Definitions and Theorems

Function: superscripts-p

(defun superscripts-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'superscripts-p))
    (declare (ignorable __function__))
    (or (not x)
        (and (acl2::keyword-listp x)
             (subsetp-equal x *opcode-map-superscripts*)))))

Function: superscripts-fix

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

Function: superscripts-equiv$inline

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

Theorem: superscripts-equiv-is-an-equivalence

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

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

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

Theorem: superscripts-fix-under-superscripts-equiv

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