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Rflagsbits

!rflagsbits->vip

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

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

Definitions and Theorems

Function: !rflagsbits->vip$inline

(defun !rflagsbits->vip$inline (vip x)
 (declare (xargs :guard (and (bitp vip) (rflagsbits-p x))))
 (mbe
   :logic
   (b* ((vip (mbe :logic (bfix vip) :exec vip))
        (x (rflagsbits-fix x)))
     (part-install vip x :width 1 :low 20))
   :exec (the (unsigned-byte 32)
              (logior (the (unsigned-byte 32)
                           (logand (the (unsigned-byte 32) x)
                                   (the (signed-byte 22) -1048577)))
                      (the (unsigned-byte 21)
                           (ash (the (unsigned-byte 1) vip)
                                20))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->vip-is-rflagsbits

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

Theorem: rflagsbits->vip-of-!rflagsbits->vip

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

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

(defthm !rflagsbits->vip-equiv-under-mask
  (b* ((?new-x (!rflagsbits->vip$inline vip x)))
    (rflagsbits-equiv-under-mask new-x x -1048577)))