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Data-segment-descriptorbits

Data-segment-descriptorbits-fix

Fixing function for data-segment-descriptorbits bit structures.

Signature
(data-segment-descriptorbits-fix x) → fty::fixed
Arguments: x — Guard (data-segment-descriptorbits-p x).
Returns: fty::fixed — Type (data-segment-descriptorbits-p fty::fixed).

Definitions and Theorems

Function: data-segment-descriptorbits-fix

(defun data-segment-descriptorbits-fix (x)
  (declare (xargs :guard (data-segment-descriptorbits-p x)))
  (let ((__function__ 'data-segment-descriptorbits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 64 x) :exec x)))

Theorem: data-segment-descriptorbits-p-of-data-segment-descriptorbits-fix

(defthm
   data-segment-descriptorbits-p-of-data-segment-descriptorbits-fix
  (b* ((fty::fixed (data-segment-descriptorbits-fix x)))
    (data-segment-descriptorbits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: data-segment-descriptorbits-fix-when-data-segment-descriptorbits-p

(defthm
 data-segment-descriptorbits-fix-when-data-segment-descriptorbits-p
 (implies (data-segment-descriptorbits-p x)
          (equal (data-segment-descriptorbits-fix x)
                 x)))

Function: data-segment-descriptorbits-equiv$inline

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

Theorem: data-segment-descriptorbits-equiv-is-an-equivalence

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

Theorem: data-segment-descriptorbits-equiv-implies-equal-data-segment-descriptorbits-fix-1

(defthm
 data-segment-descriptorbits-equiv-implies-equal-data-segment-descriptorbits-fix-1
 (implies (data-segment-descriptorbits-equiv x x-equiv)
          (equal (data-segment-descriptorbits-fix x)
                 (data-segment-descriptorbits-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: data-segment-descriptorbits-fix-under-data-segment-descriptorbits-equiv

(defthm
 data-segment-descriptorbits-fix-under-data-segment-descriptorbits-equiv
 (data-segment-descriptorbits-equiv
      (data-segment-descriptorbits-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))