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Ia32_eferbits

!ia32_eferbits->res2

Update the |X86ISA|::|RES2| field of a ia32_eferbits bit structure.

Signature
(!ia32_eferbits->res2 res2 x) → new-x
Arguments: res2 — Guard (bitp res2).; x — Guard (ia32_eferbits-p x).
Returns: new-x — Type (ia32_eferbits-p new-x).

Definitions and Theorems

Function: !ia32_eferbits->res2$inline

(defun !ia32_eferbits->res2$inline (res2 x)
  (declare (xargs :guard (and (bitp res2) (ia32_eferbits-p x))))
  (mbe :logic
       (b* ((res2 (mbe :logic (bfix res2) :exec res2))
            (x (ia32_eferbits-fix x)))
         (part-install res2 x :width 1 :low 9))
       :exec (the (unsigned-byte 12)
                  (logior (the (unsigned-byte 12)
                               (logand (the (unsigned-byte 12) x)
                                       (the (signed-byte 11) -513)))
                          (the (unsigned-byte 10)
                               (ash (the (unsigned-byte 1) res2)
                                    9))))))

Theorem: ia32_eferbits-p-of-!ia32_eferbits->res2

(defthm ia32_eferbits-p-of-!ia32_eferbits->res2
  (b* ((new-x (!ia32_eferbits->res2$inline res2 x)))
    (ia32_eferbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32_eferbits->res2$inline-of-bfix-res2

(defthm !ia32_eferbits->res2$inline-of-bfix-res2
  (equal (!ia32_eferbits->res2$inline (bfix res2)
                                      x)
         (!ia32_eferbits->res2$inline res2 x)))

Theorem: !ia32_eferbits->res2$inline-bit-equiv-congruence-on-res2

(defthm !ia32_eferbits->res2$inline-bit-equiv-congruence-on-res2
  (implies (bit-equiv res2 res2-equiv)
           (equal (!ia32_eferbits->res2$inline res2 x)
                  (!ia32_eferbits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->res2$inline-of-ia32_eferbits-fix-x

(defthm !ia32_eferbits->res2$inline-of-ia32_eferbits-fix-x
  (equal (!ia32_eferbits->res2$inline res2 (ia32_eferbits-fix x))
         (!ia32_eferbits->res2$inline res2 x)))

Theorem: !ia32_eferbits->res2$inline-ia32_eferbits-equiv-congruence-on-x

(defthm
    !ia32_eferbits->res2$inline-ia32_eferbits-equiv-congruence-on-x
  (implies (ia32_eferbits-equiv x x-equiv)
           (equal (!ia32_eferbits->res2$inline res2 x)
                  (!ia32_eferbits->res2$inline res2 x-equiv)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->res2-is-ia32_eferbits

(defthm !ia32_eferbits->res2-is-ia32_eferbits
  (equal (!ia32_eferbits->res2 res2 x)
         (change-ia32_eferbits x :res2 res2)))

Theorem: ia32_eferbits->res2-of-!ia32_eferbits->res2

(defthm ia32_eferbits->res2-of-!ia32_eferbits->res2
  (b* ((?new-x (!ia32_eferbits->res2$inline res2 x)))
    (equal (ia32_eferbits->res2 new-x)
           (bfix res2))))

Theorem: !ia32_eferbits->res2-equiv-under-mask

(defthm !ia32_eferbits->res2-equiv-under-mask
  (b* ((?new-x (!ia32_eferbits->res2$inline res2 x)))
    (ia32_eferbits-equiv-under-mask new-x x -513)))