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Cr0bits

!cr0bits->pe

Update the |ACL2|::|PE| field of a cr0bits bit structure.

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

Definitions and Theorems

Function: !cr0bits->pe$inline

(defun !cr0bits->pe$inline (pe x)
  (declare (xargs :guard (and (bitp pe) (cr0bits-p x))))
  (mbe :logic
       (b* ((pe (mbe :logic (bfix pe) :exec pe))
            (x (cr0bits-fix x)))
         (part-install pe x :width 1 :low 0))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) pe)))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr0bits->pe-is-cr0bits

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

Theorem: cr0bits->pe-of-!cr0bits->pe

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

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

(defthm !cr0bits->pe-equiv-under-mask
  (b* ((?new-x (!cr0bits->pe$inline pe x)))
    (cr0bits-equiv-under-mask new-x x -2)))