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Cr0bits

!cr0bits->em

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

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

Definitions and Theorems

Function: !cr0bits->em$inline

(defun !cr0bits->em$inline (em x)
 (declare (xargs :guard (and (bitp em) (cr0bits-p x))))
 (mbe
     :logic
     (b* ((em (mbe :logic (bfix em) :exec em))
          (x (cr0bits-fix x)))
       (part-install em x :width 1 :low 2))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 4) -5)))
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 1) em) 2))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr0bits->em-is-cr0bits

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

Theorem: cr0bits->em-of-!cr0bits->em

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

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

(defthm !cr0bits->em-equiv-under-mask
  (b* ((?new-x (!cr0bits->em$inline em x)))
    (cr0bits-equiv-under-mask new-x x -5)))