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Rflagsbits

!rflagsbits->vm

Update the |X86ISA|::|VM| field of a rflagsbits bit structure.

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

Definitions and Theorems

Function: !rflagsbits->vm$inline

(defun !rflagsbits->vm$inline (vm x)
 (declare (xargs :guard (and (bitp vm) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((vm (mbe :logic (bfix vm) :exec vm))
         (x (rflagsbits-fix x)))
      (part-install vm x :width 1 :low 17))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 19) -131073)))
                       (the (unsigned-byte 18)
                            (ash (the (unsigned-byte 1) vm) 17))))))

Theorem: rflagsbits-p-of-!rflagsbits->vm

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

Theorem: !rflagsbits->vm$inline-of-bfix-vm

(defthm !rflagsbits->vm$inline-of-bfix-vm
  (equal (!rflagsbits->vm$inline (bfix vm) x)
         (!rflagsbits->vm$inline vm x)))

Theorem: !rflagsbits->vm$inline-bit-equiv-congruence-on-vm

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

Theorem: !rflagsbits->vm$inline-of-rflagsbits-fix-x

(defthm !rflagsbits->vm$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->vm$inline vm (rflagsbits-fix x))
         (!rflagsbits->vm$inline vm x)))

Theorem: !rflagsbits->vm$inline-rflagsbits-equiv-congruence-on-x

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

Theorem: !rflagsbits->vm-is-rflagsbits

(defthm !rflagsbits->vm-is-rflagsbits
  (equal (!rflagsbits->vm vm x)
         (change-rflagsbits x :vm vm)))

Theorem: rflagsbits->vm-of-!rflagsbits->vm

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

Theorem: !rflagsbits->vm-equiv-under-mask

(defthm !rflagsbits->vm-equiv-under-mask
  (b* ((?new-x (!rflagsbits->vm$inline vm x)))
    (rflagsbits-equiv-under-mask new-x x -131073)))