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Call-gate-descriptorbits

!call-gate-descriptorbits->p

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

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

Definitions and Theorems

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

(defun !call-gate-descriptorbits->p$inline (p x)
 (declare (xargs :guard (and (bitp p)
                             (call-gate-descriptorbits-p x))))
 (mbe
     :logic
     (b* ((p (mbe :logic (bfix p) :exec p))
          (x (call-gate-descriptorbits-fix x)))
       (part-install p x :width 1 :low 47))
     :exec (the (unsigned-byte 128)
                (logior (the (unsigned-byte 128)
                             (logand (the (unsigned-byte 128) x)
                                     (the (signed-byte 49)
                                          -140737488355329)))
                        (the (unsigned-byte 48)
                             (ash (the (unsigned-byte 1) p) 47))))))

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

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

Theorem: !call-gate-descriptorbits->p$inline-of-bfix-p

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

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

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

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
             p (call-gate-descriptorbits-fix x))
        (!call-gate-descriptorbits->p$inline p 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 p x)
                 (!call-gate-descriptorbits->p$inline p x-equiv)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->p-is-call-gate-descriptorbits

(defthm !call-gate-descriptorbits->p-is-call-gate-descriptorbits
  (equal (!call-gate-descriptorbits->p p x)
         (change-call-gate-descriptorbits x
                                          :p p)))

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

(defthm call-gate-descriptorbits->p-of-!call-gate-descriptorbits->p
  (b* ((?new-x (!call-gate-descriptorbits->p$inline p x)))
    (equal (call-gate-descriptorbits->p new-x)
           (bfix p))))

Theorem: !call-gate-descriptorbits->p-equiv-under-mask

(defthm !call-gate-descriptorbits->p-equiv-under-mask
  (b* ((?new-x (!call-gate-descriptorbits->p$inline p x)))
    (call-gate-descriptorbits-equiv-under-mask
         new-x x -140737488355329)))