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System-segment-descriptorbits

System-segment-descriptorbits->res1

Access the |X86ISA|::|RES1| field of a system-segment-descriptorbits bit structure.

Signature
(system-segment-descriptorbits->res1 x) → res1
Arguments: x — Guard (system-segment-descriptorbits-p x).
Returns: res1 — Type (2bits-p res1).

Definitions and Theorems

Function: system-segment-descriptorbits->res1$inline

(defun system-segment-descriptorbits->res1$inline (x)
  (declare (xargs :guard (system-segment-descriptorbits-p x)))
  (mbe :logic
       (let ((x (system-segment-descriptorbits-fix x)))
         (part-select x :low 53 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 75)
                               (ash (the (unsigned-byte 128) x)
                                    -53))))))

Theorem: 2bits-p-of-system-segment-descriptorbits->res1

(defthm 2bits-p-of-system-segment-descriptorbits->res1
  (b* ((res1 (system-segment-descriptorbits->res1$inline x)))
    (2bits-p res1))
  :rule-classes :rewrite)

Theorem: system-segment-descriptorbits->res1$inline-of-system-segment-descriptorbits-fix-x

(defthm
 system-segment-descriptorbits->res1$inline-of-system-segment-descriptorbits-fix-x
 (equal (system-segment-descriptorbits->res1$inline
             (system-segment-descriptorbits-fix x))
        (system-segment-descriptorbits->res1$inline x)))

Theorem: system-segment-descriptorbits->res1$inline-system-segment-descriptorbits-equiv-congruence-on-x

(defthm
 system-segment-descriptorbits->res1$inline-system-segment-descriptorbits-equiv-congruence-on-x
 (implies
      (system-segment-descriptorbits-equiv x x-equiv)
      (equal (system-segment-descriptorbits->res1$inline x)
             (system-segment-descriptorbits->res1$inline x-equiv)))
 :rule-classes :congruence)

Theorem: system-segment-descriptorbits->res1-of-system-segment-descriptorbits

(defthm
 system-segment-descriptorbits->res1-of-system-segment-descriptorbits
 (equal (system-segment-descriptorbits->res1
             (system-segment-descriptorbits
                  limit15-0 base15-0 base23-16 type
                  s dpl p limit19-16 avl res1 g base31-24
                  base63-32 res2 all-zeroes? res3))
        (2bits-fix res1)))

Theorem: system-segment-descriptorbits->res1-of-write-with-mask

(defthm system-segment-descriptorbits->res1-of-write-with-mask
 (implies
  (and
      (fty::bitstruct-read-over-write-hyps
           x
           system-segment-descriptorbits-equiv-under-mask)
      (system-segment-descriptorbits-equiv-under-mask x y fty::mask)
      (equal (logand (lognot fty::mask)
                     27021597764222976)
             0))
  (equal (system-segment-descriptorbits->res1 x)
         (system-segment-descriptorbits->res1 y))))