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Call-gate-descriptorbits

!call-gate-descriptorbits->res3

Update the |X86ISA|::|RES3| field of a call-gate-descriptorbits bit structure.

Signature
(!call-gate-descriptorbits->res3 res3 x) → new-x
Arguments: res3 — Guard (19bits-p res3).; x — Guard (call-gate-descriptorbits-p x).
Returns: new-x — Type (call-gate-descriptorbits-p new-x).

Definitions and Theorems

Function: !call-gate-descriptorbits->res3$inline

(defun !call-gate-descriptorbits->res3$inline (res3 x)
 (declare (xargs :guard (and (19bits-p res3)
                             (call-gate-descriptorbits-p x))))
 (mbe
  :logic
  (b* ((res3 (mbe :logic (19bits-fix res3)
                  :exec res3))
       (x (call-gate-descriptorbits-fix x)))
    (part-install res3 x
                  :width 19
                  :low 109))
  :exec
  (the
   (unsigned-byte 128)
   (logior
       (the (unsigned-byte 128)
            (logand (the (unsigned-byte 128) x)
                    (the (signed-byte 129)
                         -340281717883831146609921041119727058945)))
       (the (unsigned-byte 128)
            (ash (the (unsigned-byte 19) res3)
                 109))))))

Theorem: call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res3

(defthm
      call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res3
  (b* ((new-x (!call-gate-descriptorbits->res3$inline res3 x)))
    (call-gate-descriptorbits-p new-x))
  :rule-classes :rewrite)

Theorem: !call-gate-descriptorbits->res3$inline-of-19bits-fix-res3

(defthm !call-gate-descriptorbits->res3$inline-of-19bits-fix-res3
  (equal (!call-gate-descriptorbits->res3$inline (19bits-fix res3)
                                                 x)
         (!call-gate-descriptorbits->res3$inline res3 x)))

Theorem: !call-gate-descriptorbits->res3$inline-19bits-equiv-congruence-on-res3

(defthm
 !call-gate-descriptorbits->res3$inline-19bits-equiv-congruence-on-res3
 (implies
      (19bits-equiv res3 res3-equiv)
      (equal (!call-gate-descriptorbits->res3$inline res3 x)
             (!call-gate-descriptorbits->res3$inline res3-equiv x)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res3$inline-of-call-gate-descriptorbits-fix-x

(defthm
 !call-gate-descriptorbits->res3$inline-of-call-gate-descriptorbits-fix-x
 (equal (!call-gate-descriptorbits->res3$inline
             res3 (call-gate-descriptorbits-fix x))
        (!call-gate-descriptorbits->res3$inline res3 x)))

Theorem: !call-gate-descriptorbits->res3$inline-call-gate-descriptorbits-equiv-congruence-on-x

(defthm
 !call-gate-descriptorbits->res3$inline-call-gate-descriptorbits-equiv-congruence-on-x
 (implies
      (call-gate-descriptorbits-equiv x x-equiv)
      (equal (!call-gate-descriptorbits->res3$inline res3 x)
             (!call-gate-descriptorbits->res3$inline res3 x-equiv)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res3-is-call-gate-descriptorbits

(defthm !call-gate-descriptorbits->res3-is-call-gate-descriptorbits
  (equal (!call-gate-descriptorbits->res3 res3 x)
         (change-call-gate-descriptorbits x
                                          :res3 res3)))

Theorem: call-gate-descriptorbits->res3-of-!call-gate-descriptorbits->res3

(defthm
  call-gate-descriptorbits->res3-of-!call-gate-descriptorbits->res3
  (b* ((?new-x (!call-gate-descriptorbits->res3$inline res3 x)))
    (equal (call-gate-descriptorbits->res3 new-x)
           (19bits-fix res3))))

Theorem: !call-gate-descriptorbits->res3-equiv-under-mask

(defthm !call-gate-descriptorbits->res3-equiv-under-mask
  (b* ((?new-x (!call-gate-descriptorbits->res3$inline res3 x)))
    (call-gate-descriptorbits-equiv-under-mask
         new-x
         x 649037107316853453566312041152511)))