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Call-gate-descriptorbits

Call-gate-descriptorbits->p

Access the |ACL2|::|P| field of a call-gate-descriptorbits bit structure.

Signature
(call-gate-descriptorbits->p x) → p
Arguments: x — Guard (call-gate-descriptorbits-p x).
Returns: p — Type (bitp p).

Definitions and Theorems

Function: call-gate-descriptorbits->p$inline

(defun call-gate-descriptorbits->p$inline (x)
  (declare (xargs :guard (call-gate-descriptorbits-p x)))
  (mbe :logic
       (let ((x (call-gate-descriptorbits-fix x)))
         (part-select x :low 47 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 81)
                               (ash (the (unsigned-byte 128) x)
                                    -47))))))

Theorem: bitp-of-call-gate-descriptorbits->p

(defthm bitp-of-call-gate-descriptorbits->p
  (b* ((p (call-gate-descriptorbits->p$inline x)))
    (bitp p))
  :rule-classes :rewrite)

Theorem: call-gate-descriptorbits->p$inline-of-call-gate-descriptorbits-fix-x

(defthm
 call-gate-descriptorbits->p$inline-of-call-gate-descriptorbits-fix-x
 (equal (call-gate-descriptorbits->p$inline
             (call-gate-descriptorbits-fix x))
        (call-gate-descriptorbits->p$inline x)))

Theorem: call-gate-descriptorbits->p$inline-call-gate-descriptorbits-equiv-congruence-on-x

(defthm
 call-gate-descriptorbits->p$inline-call-gate-descriptorbits-equiv-congruence-on-x
 (implies (call-gate-descriptorbits-equiv x x-equiv)
          (equal (call-gate-descriptorbits->p$inline x)
                 (call-gate-descriptorbits->p$inline x-equiv)))
 :rule-classes :congruence)

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

(defthm call-gate-descriptorbits->p-of-call-gate-descriptorbits
 (equal
  (call-gate-descriptorbits->p
    (call-gate-descriptorbits offset15-0
                              selector res1 type s dpl p offset31-16
                              offset63-32 res2 all-zeroes? res3))
  (bfix p)))

Theorem: call-gate-descriptorbits->p-of-write-with-mask

(defthm call-gate-descriptorbits->p-of-write-with-mask
 (implies
      (and (fty::bitstruct-read-over-write-hyps
                x
                call-gate-descriptorbits-equiv-under-mask)
           (call-gate-descriptorbits-equiv-under-mask x y fty::mask)
           (equal (logand (lognot fty::mask)
                          140737488355328)
                  0))
      (equal (call-gate-descriptorbits->p x)
             (call-gate-descriptorbits->p y))))