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Cr0bits

!cr0bits->am

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

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

Definitions and Theorems

Function: !cr0bits->am$inline

(defun !cr0bits->am$inline (am x)
 (declare (xargs :guard (and (bitp am) (cr0bits-p x))))
 (mbe
    :logic
    (b* ((am (mbe :logic (bfix am) :exec am))
         (x (cr0bits-fix x)))
      (part-install am x :width 1 :low 18))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 20) -262145)))
                       (the (unsigned-byte 19)
                            (ash (the (unsigned-byte 1) am) 18))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr0bits->am-is-cr0bits

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

Theorem: cr0bits->am-of-!cr0bits->am

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

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

(defthm !cr0bits->am-equiv-under-mask
  (b* ((?new-x (!cr0bits->am$inline am x)))
    (cr0bits-equiv-under-mask new-x x -262145)))