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Ia32e-pdpte-1gb-pagebits

!ia32e-pdpte-1gb-pagebits->u/s

Update the |X86ISA|::|U/S| field of a ia32e-pdpte-1gb-pagebits bit structure.

Signature
(!ia32e-pdpte-1gb-pagebits->u/s u/s x) → new-x
Arguments: u/s — Guard (bitp u/s).; x — Guard (ia32e-pdpte-1gb-pagebits-p x).
Returns: new-x — Type (ia32e-pdpte-1gb-pagebits-p new-x).

Definitions and Theorems

Function: !ia32e-pdpte-1gb-pagebits->u/s$inline

(defun !ia32e-pdpte-1gb-pagebits->u/s$inline (u/s x)
 (declare (xargs :guard (and (bitp u/s)
                             (ia32e-pdpte-1gb-pagebits-p x))))
 (mbe
    :logic
    (b* ((u/s (mbe :logic (bfix u/s) :exec u/s))
         (x (ia32e-pdpte-1gb-pagebits-fix x)))
      (part-install u/s x :width 1 :low 2))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 4) -5)))
                       (the (unsigned-byte 3)
                            (ash (the (unsigned-byte 1) u/s) 2))))))

Theorem: ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->u/s

(defthm ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->u/s
  (b* ((new-x (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)))
    (ia32e-pdpte-1gb-pagebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pdpte-1gb-pagebits->u/s$inline-of-bfix-u/s

(defthm !ia32e-pdpte-1gb-pagebits->u/s$inline-of-bfix-u/s
  (equal (!ia32e-pdpte-1gb-pagebits->u/s$inline (bfix u/s)
                                                x)
         (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)))

Theorem: !ia32e-pdpte-1gb-pagebits->u/s$inline-bit-equiv-congruence-on-u/s

(defthm
  !ia32e-pdpte-1gb-pagebits->u/s$inline-bit-equiv-congruence-on-u/s
  (implies
       (bit-equiv u/s u/s-equiv)
       (equal (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)
              (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->u/s$inline-of-ia32e-pdpte-1gb-pagebits-fix-x

(defthm
 !ia32e-pdpte-1gb-pagebits->u/s$inline-of-ia32e-pdpte-1gb-pagebits-fix-x
 (equal (!ia32e-pdpte-1gb-pagebits->u/s$inline
             u/s (ia32e-pdpte-1gb-pagebits-fix x))
        (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)))

Theorem: !ia32e-pdpte-1gb-pagebits->u/s$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x

(defthm
 !ia32e-pdpte-1gb-pagebits->u/s$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x
 (implies
      (ia32e-pdpte-1gb-pagebits-equiv x x-equiv)
      (equal (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)
             (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->u/s-is-ia32e-pdpte-1gb-pagebits

(defthm !ia32e-pdpte-1gb-pagebits->u/s-is-ia32e-pdpte-1gb-pagebits
  (equal (!ia32e-pdpte-1gb-pagebits->u/s u/s x)
         (change-ia32e-pdpte-1gb-pagebits x
                                          :u/s u/s)))

Theorem: ia32e-pdpte-1gb-pagebits->u/s-of-!ia32e-pdpte-1gb-pagebits->u/s

(defthm
    ia32e-pdpte-1gb-pagebits->u/s-of-!ia32e-pdpte-1gb-pagebits->u/s
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)))
    (equal (ia32e-pdpte-1gb-pagebits->u/s new-x)
           (bfix u/s))))

Theorem: !ia32e-pdpte-1gb-pagebits->u/s-equiv-under-mask

(defthm !ia32e-pdpte-1gb-pagebits->u/s-equiv-under-mask
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->u/s$inline u/s x)))
    (ia32e-pdpte-1gb-pagebits-equiv-under-mask new-x x -5)))