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Op-mode-p

Signature
(op-mode-p x) → *

Definitions and Theorems

Function: op-mode-p

(defun op-mode-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'op-mode-p))
    (declare (ignorable __function__))
    (or (not x)
        (member-equal x '(:o64 :i64)))))

Function: op-mode-fix

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

Function: op-mode-equiv$inline

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

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

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

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

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

Theorem: op-mode-fix-under-op-mode-equiv

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