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System-segment-descriptorbits

!system-segment-descriptorbits->res1

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

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

Definitions and Theorems

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

(defun !system-segment-descriptorbits->res1$inline (res1 x)
  (declare (xargs :guard (and (2bits-p res1)
                              (system-segment-descriptorbits-p x))))
  (mbe :logic
       (b* ((res1 (mbe :logic (2bits-fix res1)
                       :exec res1))
            (x (system-segment-descriptorbits-fix x)))
         (part-install res1 x :width 2 :low 53))
       :exec (the (unsigned-byte 128)
                  (logior (the (unsigned-byte 128)
                               (logand (the (unsigned-byte 128) x)
                                       (the (signed-byte 56)
                                            -27021597764222977)))
                          (the (unsigned-byte 55)
                               (ash (the (unsigned-byte 2) res1)
                                    53))))))

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

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

Theorem: !system-segment-descriptorbits->res1$inline-of-2bits-fix-res1

(defthm
      !system-segment-descriptorbits->res1$inline-of-2bits-fix-res1
  (equal
       (!system-segment-descriptorbits->res1$inline (2bits-fix res1)
                                                    x)
       (!system-segment-descriptorbits->res1$inline res1 x)))

Theorem: !system-segment-descriptorbits->res1$inline-2bits-equiv-congruence-on-res1

(defthm
 !system-segment-descriptorbits->res1$inline-2bits-equiv-congruence-on-res1
 (implies
   (2bits-equiv res1 res1-equiv)
   (equal
        (!system-segment-descriptorbits->res1$inline res1 x)
        (!system-segment-descriptorbits->res1$inline res1-equiv x)))
 :rule-classes :congruence)

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
             res1
             (system-segment-descriptorbits-fix x))
        (!system-segment-descriptorbits->res1$inline res1 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 res1 x)
        (!system-segment-descriptorbits->res1$inline res1 x-equiv)))
 :rule-classes :congruence)

Theorem: !system-segment-descriptorbits->res1-is-system-segment-descriptorbits

(defthm
 !system-segment-descriptorbits->res1-is-system-segment-descriptorbits
 (equal (!system-segment-descriptorbits->res1 res1 x)
        (change-system-segment-descriptorbits x
                                              :res1 res1)))

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

(defthm
 system-segment-descriptorbits->res1-of-!system-segment-descriptorbits->res1
 (b* ((?new-x (!system-segment-descriptorbits->res1$inline res1 x)))
   (equal (system-segment-descriptorbits->res1 new-x)
          (2bits-fix res1))))

Theorem: !system-segment-descriptorbits->res1-equiv-under-mask

(defthm !system-segment-descriptorbits->res1-equiv-under-mask
 (b* ((?new-x (!system-segment-descriptorbits->res1$inline res1 x)))
   (system-segment-descriptorbits-equiv-under-mask
        new-x x -27021597764222977)))