		Search-engine friendly clone of the ACL2 documentation.

Cr4bits

!cr4bits->res1

Update the |X86ISA|::|RES1| field of a cr4bits bit structure.

Signature
(!cr4bits->res1 res1 x) → new-x
Arguments: res1 — Guard (bitp res1).; x — Guard (cr4bits-p x).
Returns: new-x — Type (cr4bits-p new-x).

Definitions and Theorems

Function: !cr4bits->res1$inline

(defun !cr4bits->res1$inline (res1 x)
 (declare (xargs :guard (and (bitp res1) (cr4bits-p x))))
 (mbe
     :logic
     (b* ((res1 (mbe :logic (bfix res1) :exec res1))
          (x (cr4bits-fix x)))
       (part-install res1 x :width 1 :low 15))
     :exec (the (unsigned-byte 26)
                (logior (the (unsigned-byte 26)
                             (logand (the (unsigned-byte 26) x)
                                     (the (signed-byte 17) -32769)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 1) res1)
                                  15))))))

Theorem: cr4bits-p-of-!cr4bits->res1

(defthm cr4bits-p-of-!cr4bits->res1
  (b* ((new-x (!cr4bits->res1$inline res1 x)))
    (cr4bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr4bits->res1$inline-of-bfix-res1

(defthm !cr4bits->res1$inline-of-bfix-res1
  (equal (!cr4bits->res1$inline (bfix res1) x)
         (!cr4bits->res1$inline res1 x)))

Theorem: !cr4bits->res1$inline-bit-equiv-congruence-on-res1

(defthm !cr4bits->res1$inline-bit-equiv-congruence-on-res1
  (implies (bit-equiv res1 res1-equiv)
           (equal (!cr4bits->res1$inline res1 x)
                  (!cr4bits->res1$inline res1-equiv x)))
  :rule-classes :congruence)

Theorem: !cr4bits->res1$inline-of-cr4bits-fix-x

(defthm !cr4bits->res1$inline-of-cr4bits-fix-x
  (equal (!cr4bits->res1$inline res1 (cr4bits-fix x))
         (!cr4bits->res1$inline res1 x)))

Theorem: !cr4bits->res1$inline-cr4bits-equiv-congruence-on-x

(defthm !cr4bits->res1$inline-cr4bits-equiv-congruence-on-x
  (implies (cr4bits-equiv x x-equiv)
           (equal (!cr4bits->res1$inline res1 x)
                  (!cr4bits->res1$inline res1 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr4bits->res1-is-cr4bits

(defthm !cr4bits->res1-is-cr4bits
  (equal (!cr4bits->res1 res1 x)
         (change-cr4bits x :res1 res1)))

Theorem: cr4bits->res1-of-!cr4bits->res1

(defthm cr4bits->res1-of-!cr4bits->res1
  (b* ((?new-x (!cr4bits->res1$inline res1 x)))
    (equal (cr4bits->res1 new-x)
           (bfix res1))))

Theorem: !cr4bits->res1-equiv-under-mask

(defthm !cr4bits->res1-equiv-under-mask
  (b* ((?new-x (!cr4bits->res1$inline res1 x)))
    (cr4bits-equiv-under-mask new-x x -32769)))