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Cr0bits

!cr0bits->res2

Update the |X86ISA|::|RES2| field of a cr0bits bit structure.

Signature
(!cr0bits->res2 res2 x) → new-x
Arguments: res2 — Guard (bitp res2).; x — Guard (cr0bits-p x).
Returns: new-x — Type (cr0bits-p new-x).

Definitions and Theorems

Function: !cr0bits->res2$inline

(defun !cr0bits->res2$inline (res2 x)
 (declare (xargs :guard (and (bitp res2) (cr0bits-p x))))
 (mbe
    :logic
    (b* ((res2 (mbe :logic (bfix res2) :exec res2))
         (x (cr0bits-fix x)))
      (part-install res2 x :width 1 :low 17))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 19) -131073)))
                       (the (unsigned-byte 18)
                            (ash (the (unsigned-byte 1) res2)
                                 17))))))

Theorem: cr0bits-p-of-!cr0bits->res2

(defthm cr0bits-p-of-!cr0bits->res2
  (b* ((new-x (!cr0bits->res2$inline res2 x)))
    (cr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr0bits->res2$inline-of-bfix-res2

(defthm !cr0bits->res2$inline-of-bfix-res2
  (equal (!cr0bits->res2$inline (bfix res2) x)
         (!cr0bits->res2$inline res2 x)))

Theorem: !cr0bits->res2$inline-bit-equiv-congruence-on-res2

(defthm !cr0bits->res2$inline-bit-equiv-congruence-on-res2
  (implies (bit-equiv res2 res2-equiv)
           (equal (!cr0bits->res2$inline res2 x)
                  (!cr0bits->res2$inline res2-equiv x)))
  :rule-classes :congruence)

Theorem: !cr0bits->res2$inline-of-cr0bits-fix-x

(defthm !cr0bits->res2$inline-of-cr0bits-fix-x
  (equal (!cr0bits->res2$inline res2 (cr0bits-fix x))
         (!cr0bits->res2$inline res2 x)))

Theorem: !cr0bits->res2$inline-cr0bits-equiv-congruence-on-x

(defthm !cr0bits->res2$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (!cr0bits->res2$inline res2 x)
                  (!cr0bits->res2$inline res2 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->res2-is-cr0bits

(defthm !cr0bits->res2-is-cr0bits
  (equal (!cr0bits->res2 res2 x)
         (change-cr0bits x :res2 res2)))

Theorem: cr0bits->res2-of-!cr0bits->res2

(defthm cr0bits->res2-of-!cr0bits->res2
  (b* ((?new-x (!cr0bits->res2$inline res2 x)))
    (equal (cr0bits->res2 new-x)
           (bfix res2))))

Theorem: !cr0bits->res2-equiv-under-mask

(defthm !cr0bits->res2-equiv-under-mask
  (b* ((?new-x (!cr0bits->res2$inline res2 x)))
    (cr0bits-equiv-under-mask new-x x -131073)))