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System-segment-descriptorbits

System-segment-descriptorbits-fix

Fixing function for system-segment-descriptorbits bit structures.

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

Definitions and Theorems

Function: system-segment-descriptorbits-fix

(defun system-segment-descriptorbits-fix (x)
  (declare (xargs :guard (system-segment-descriptorbits-p x)))
  (let ((__function__ 'system-segment-descriptorbits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 128 x) :exec x)))

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

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

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

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

Function: system-segment-descriptorbits-equiv$inline

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

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

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

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

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

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

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