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Call-gate-descriptorbits

!call-gate-descriptorbits->res1

Update the |X86ISA|::|RES1| field of a call-gate-descriptorbits bit structure.

Signature
(!call-gate-descriptorbits->res1 res1 x) → new-x
Arguments: res1 — Guard (8bits-p res1).; x — Guard (call-gate-descriptorbits-p x).
Returns: new-x — Type (call-gate-descriptorbits-p new-x).

Definitions and Theorems

Function: !call-gate-descriptorbits->res1$inline

(defun !call-gate-descriptorbits->res1$inline (res1 x)
 (declare (xargs :guard (and (8bits-p res1)
                             (call-gate-descriptorbits-p x))))
 (mbe
   :logic
   (b* ((res1 (mbe :logic (8bits-fix res1)
                   :exec res1))
        (x (call-gate-descriptorbits-fix x)))
     (part-install res1 x :width 8 :low 32))
   :exec
   (the (unsigned-byte 128)
        (logior (the (unsigned-byte 128)
                     (logand (the (unsigned-byte 128) x)
                             (the (signed-byte 41) -1095216660481)))
                (the (unsigned-byte 40)
                     (ash (the (unsigned-byte 8) res1)
                          32))))))

Theorem: call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res1

(defthm
      call-gate-descriptorbits-p-of-!call-gate-descriptorbits->res1
  (b* ((new-x (!call-gate-descriptorbits->res1$inline res1 x)))
    (call-gate-descriptorbits-p new-x))
  :rule-classes :rewrite)

Theorem: !call-gate-descriptorbits->res1$inline-of-8bits-fix-res1

(defthm !call-gate-descriptorbits->res1$inline-of-8bits-fix-res1
  (equal (!call-gate-descriptorbits->res1$inline (8bits-fix res1)
                                                 x)
         (!call-gate-descriptorbits->res1$inline res1 x)))

Theorem: !call-gate-descriptorbits->res1$inline-8bits-equiv-congruence-on-res1

(defthm
 !call-gate-descriptorbits->res1$inline-8bits-equiv-congruence-on-res1
 (implies
      (8bits-equiv res1 res1-equiv)
      (equal (!call-gate-descriptorbits->res1$inline res1 x)
             (!call-gate-descriptorbits->res1$inline res1-equiv x)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res1$inline-of-call-gate-descriptorbits-fix-x

(defthm
 !call-gate-descriptorbits->res1$inline-of-call-gate-descriptorbits-fix-x
 (equal (!call-gate-descriptorbits->res1$inline
             res1 (call-gate-descriptorbits-fix x))
        (!call-gate-descriptorbits->res1$inline res1 x)))

Theorem: !call-gate-descriptorbits->res1$inline-call-gate-descriptorbits-equiv-congruence-on-x

(defthm
 !call-gate-descriptorbits->res1$inline-call-gate-descriptorbits-equiv-congruence-on-x
 (implies
      (call-gate-descriptorbits-equiv x x-equiv)
      (equal (!call-gate-descriptorbits->res1$inline res1 x)
             (!call-gate-descriptorbits->res1$inline res1 x-equiv)))
 :rule-classes :congruence)

Theorem: !call-gate-descriptorbits->res1-is-call-gate-descriptorbits

(defthm !call-gate-descriptorbits->res1-is-call-gate-descriptorbits
  (equal (!call-gate-descriptorbits->res1 res1 x)
         (change-call-gate-descriptorbits x
                                          :res1 res1)))

Theorem: call-gate-descriptorbits->res1-of-!call-gate-descriptorbits->res1

(defthm
  call-gate-descriptorbits->res1-of-!call-gate-descriptorbits->res1
  (b* ((?new-x (!call-gate-descriptorbits->res1$inline res1 x)))
    (equal (call-gate-descriptorbits->res1 new-x)
           (8bits-fix res1))))

Theorem: !call-gate-descriptorbits->res1-equiv-under-mask

(defthm !call-gate-descriptorbits->res1-equiv-under-mask
  (b* ((?new-x (!call-gate-descriptorbits->res1$inline res1 x)))
    (call-gate-descriptorbits-equiv-under-mask
         new-x x -1095216660481)))