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Cr4bits

!cr4bits->osfxsr

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

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

Definitions and Theorems

Function: !cr4bits->osfxsr$inline

(defun !cr4bits->osfxsr$inline (osfxsr x)
  (declare (xargs :guard (and (bitp osfxsr) (cr4bits-p x))))
  (mbe :logic
       (b* ((osfxsr (mbe :logic (bfix osfxsr) :exec osfxsr))
            (x (cr4bits-fix x)))
         (part-install osfxsr x :width 1 :low 9))
       :exec (the (unsigned-byte 26)
                  (logior (the (unsigned-byte 26)
                               (logand (the (unsigned-byte 26) x)
                                       (the (signed-byte 11) -513)))
                          (the (unsigned-byte 10)
                               (ash (the (unsigned-byte 1) osfxsr)
                                    9))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->osfxsr-is-cr4bits

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

Theorem: cr4bits->osfxsr-of-!cr4bits->osfxsr

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

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

(defthm !cr4bits->osfxsr-equiv-under-mask
  (b* ((?new-x (!cr4bits->osfxsr$inline osfxsr x)))
    (cr4bits-equiv-under-mask new-x x -513)))