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Call-gate-descriptorbits

!call-gate-descriptorbits->res2

Update the |X86ISA|::|RES2| field of a call-gate-descriptorbits bit structure.

Signature
(!call-gate-descriptorbits->res2 res2 x) → new-x
Arguments: res2 — Guard (8bits-p res2).; x — Guard (call-gate-descriptorbits-p x).
Returns: new-x — Type (call-gate-descriptorbits-p new-x).

Definitions and Theorems

Function: !call-gate-descriptorbits->res2$inline

(defun !call-gate-descriptorbits->res2$inline (res2 x)
 (declare (xargs :guard (and (8bits-p res2)
                             (call-gate-descriptorbits-p x))))
 (mbe
  :logic
  (b* ((res2 (mbe :logic (8bits-fix res2)
                  :exec res2))
       (x (call-gate-descriptorbits-fix x)))
    (part-install res2 x :width 8 :low 96))
  :exec
  (the
      (unsigned-byte 128)
      (logior (the (unsigned-byte 128)
                   (logand (the (unsigned-byte 128) x)
                           (the (signed-byte 105)
                                -20203181441137406086353707335681)))
              (the (unsigned-byte 104)
                   (ash (the (unsigned-byte 8) res2)
                        96))))))

Theorem: call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res2

(defthm
      call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res2
  (b* ((new-x (!call-gate-descriptorbits->res2$inline res2 x)))
    (call-gate-descriptorbits-p new-x))
  :rule-classes :rewrite)

Theorem: !call-gate-descriptorbits->res2$inline-of-8bits-fix-res2

(defthm !call-gate-descriptorbits->res2$inline-of-8bits-fix-res2
  (equal (!call-gate-descriptorbits->res2$inline (8bits-fix res2)
                                                 x)
         (!call-gate-descriptorbits->res2$inline res2 x)))

Theorem: !call-gate-descriptorbits->res2$inline-8bits-equiv-congruence-on-res2

(defthm
 !call-gate-descriptorbits->res2$inline-8bits-equiv-congruence-on-res2
 (implies
      (8bits-equiv res2 res2-equiv)
      (equal (!call-gate-descriptorbits->res2$inline res2 x)
             (!call-gate-descriptorbits->res2$inline res2-equiv x)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res2$inline-of-call-gate-descriptorbits-fix-x

(defthm
 !call-gate-descriptorbits->res2$inline-of-call-gate-descriptorbits-fix-x
 (equal (!call-gate-descriptorbits->res2$inline
             res2 (call-gate-descriptorbits-fix x))
        (!call-gate-descriptorbits->res2$inline res2 x)))

Theorem: !call-gate-descriptorbits->res2$inline-call-gate-descriptorbits-equiv-congruence-on-x

(defthm
 !call-gate-descriptorbits->res2$inline-call-gate-descriptorbits-equiv-congruence-on-x
 (implies
      (call-gate-descriptorbits-equiv x x-equiv)
      (equal (!call-gate-descriptorbits->res2$inline res2 x)
             (!call-gate-descriptorbits->res2$inline res2 x-equiv)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res2-is-call-gate-descriptorbits

(defthm !call-gate-descriptorbits->res2-is-call-gate-descriptorbits
  (equal (!call-gate-descriptorbits->res2 res2 x)
         (change-call-gate-descriptorbits x
                                          :res2 res2)))

Theorem: call-gate-descriptorbits->res2-of-!call-gate-descriptorbits->res2

(defthm
  call-gate-descriptorbits->res2-of-!call-gate-descriptorbits->res2
  (b* ((?new-x (!call-gate-descriptorbits->res2$inline res2 x)))
    (equal (call-gate-descriptorbits->res2 new-x)
           (8bits-fix res2))))

Theorem: !call-gate-descriptorbits->res2-equiv-under-mask

(defthm !call-gate-descriptorbits->res2-equiv-under-mask
  (b* ((?new-x (!call-gate-descriptorbits->res2$inline res2 x)))
    (call-gate-descriptorbits-equiv-under-mask
         new-x
         x -20203181441137406086353707335681)))