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Op-pfx-p

Signature
(op-pfx-p x) → *

Definitions and Theorems

Function: op-pfx-p

(defun op-pfx-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'op-pfx-p))
    (declare (ignorable __function__))
    (or (not x)
        (member-equal x
                      '(:no-prefix :|66|
                                   :f3 :f2
                                   :v :v66
                                   :vf3 :vf2
                                   :ev :ev66
                                   :evf3 :evf2)))))

Function: op-pfx-fix

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

Function: op-pfx-equiv$inline

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

Theorem: op-pfx-equiv-is-an-equivalence

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

Theorem: op-pfx-equiv-implies-equal-op-pfx-fix-1

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

Theorem: op-pfx-fix-under-op-pfx-equiv

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