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Call-gate-descriptorbits

Call-gate-descriptorbits-fix

Fixing function for call-gate-descriptorbits bit structures.

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

Definitions and Theorems

Function: call-gate-descriptorbits-fix

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

Theorem: call-gate-descriptorbits-p-of-call-gate-descriptorbits-fix

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

Theorem: call-gate-descriptorbits-fix-when-call-gate-descriptorbits-p

(defthm call-gate-descriptorbits-fix-when-call-gate-descriptorbits-p
  (implies (call-gate-descriptorbits-p x)
           (equal (call-gate-descriptorbits-fix x)
                  x)))

Function: call-gate-descriptorbits-equiv$inline

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

Theorem: call-gate-descriptorbits-equiv-is-an-equivalence

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

Theorem: call-gate-descriptorbits-equiv-implies-equal-call-gate-descriptorbits-fix-1

(defthm
 call-gate-descriptorbits-equiv-implies-equal-call-gate-descriptorbits-fix-1
 (implies (call-gate-descriptorbits-equiv x x-equiv)
          (equal (call-gate-descriptorbits-fix x)
                 (call-gate-descriptorbits-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: call-gate-descriptorbits-fix-under-call-gate-descriptorbits-equiv

(defthm
  call-gate-descriptorbits-fix-under-call-gate-descriptorbits-equiv
  (call-gate-descriptorbits-equiv (call-gate-descriptorbits-fix x)
                                  x)
  :rule-classes (:rewrite :rewrite-quoted-constant))