		Search-engine friendly clone of the ACL2 documentation.

Cr4bits

!cr4bits->vme

Update the |X86ISA|::|VME| field of a cr4bits bit structure.

Signature
(!cr4bits->vme vme x) → new-x
Arguments: vme — Guard (bitp vme).; x — Guard (cr4bits-p x).
Returns: new-x — Type (cr4bits-p new-x).

Definitions and Theorems

Function: !cr4bits->vme$inline

(defun !cr4bits->vme$inline (vme x)
  (declare (xargs :guard (and (bitp vme) (cr4bits-p x))))
  (mbe :logic
       (b* ((vme (mbe :logic (bfix vme) :exec vme))
            (x (cr4bits-fix x)))
         (part-install vme x :width 1 :low 0))
       :exec (the (unsigned-byte 26)
                  (logior (the (unsigned-byte 26)
                               (logand (the (unsigned-byte 26) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) vme)))))

Theorem: cr4bits-p-of-!cr4bits->vme

(defthm cr4bits-p-of-!cr4bits->vme
  (b* ((new-x (!cr4bits->vme$inline vme x)))
    (cr4bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr4bits->vme$inline-of-bfix-vme

(defthm !cr4bits->vme$inline-of-bfix-vme
  (equal (!cr4bits->vme$inline (bfix vme) x)
         (!cr4bits->vme$inline vme x)))

Theorem: !cr4bits->vme$inline-bit-equiv-congruence-on-vme

(defthm !cr4bits->vme$inline-bit-equiv-congruence-on-vme
  (implies (bit-equiv vme vme-equiv)
           (equal (!cr4bits->vme$inline vme x)
                  (!cr4bits->vme$inline vme-equiv x)))
  :rule-classes :congruence)

Theorem: !cr4bits->vme$inline-of-cr4bits-fix-x

(defthm !cr4bits->vme$inline-of-cr4bits-fix-x
  (equal (!cr4bits->vme$inline vme (cr4bits-fix x))
         (!cr4bits->vme$inline vme x)))

Theorem: !cr4bits->vme$inline-cr4bits-equiv-congruence-on-x

(defthm !cr4bits->vme$inline-cr4bits-equiv-congruence-on-x
  (implies (cr4bits-equiv x x-equiv)
           (equal (!cr4bits->vme$inline vme x)
                  (!cr4bits->vme$inline vme x-equiv)))
  :rule-classes :congruence)

Theorem: !cr4bits->vme-is-cr4bits

(defthm !cr4bits->vme-is-cr4bits
  (equal (!cr4bits->vme vme x)
         (change-cr4bits x :vme vme)))

Theorem: cr4bits->vme-of-!cr4bits->vme

(defthm cr4bits->vme-of-!cr4bits->vme
  (b* ((?new-x (!cr4bits->vme$inline vme x)))
    (equal (cr4bits->vme new-x)
           (bfix vme))))

Theorem: !cr4bits->vme-equiv-under-mask

(defthm !cr4bits->vme-equiv-under-mask
  (b* ((?new-x (!cr4bits->vme$inline vme x)))
    (cr4bits-equiv-under-mask new-x x -2)))