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Ia32e-pml4ebits

!ia32e-pml4ebits->u/s

Update the |X86ISA|::|U/S| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->u/s u/s x) → new-x
Arguments: u/s — Guard (bitp u/s).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->u/s$inline

(defun
 !ia32e-pml4ebits->u/s$inline (u/s x)
 (declare (xargs :guard (and (bitp u/s) (ia32e-pml4ebits-p x))))
 (mbe
    :logic (b* ((u/s (mbe :logic (bfix u/s) :exec u/s))
                (x (ia32e-pml4ebits-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-pml4ebits-p-of-!ia32e-pml4ebits->u/s

(defthm ia32e-pml4ebits-p-of-!ia32e-pml4ebits->u/s
        (b* ((new-x (!ia32e-pml4ebits->u/s$inline u/s x)))
            (ia32e-pml4ebits-p new-x))
        :rule-classes :rewrite)

Theorem: !ia32e-pml4ebits->u/s$inline-of-bfix-u/s

(defthm !ia32e-pml4ebits->u/s$inline-of-bfix-u/s
        (equal (!ia32e-pml4ebits->u/s$inline (bfix u/s)
                                             x)
               (!ia32e-pml4ebits->u/s$inline u/s x)))

Theorem: !ia32e-pml4ebits->u/s$inline-bit-equiv-congruence-on-u/s

(defthm !ia32e-pml4ebits->u/s$inline-bit-equiv-congruence-on-u/s
        (implies (bit-equiv u/s u/s-equiv)
                 (equal (!ia32e-pml4ebits->u/s$inline u/s x)
                        (!ia32e-pml4ebits->u/s$inline u/s-equiv x)))
        :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->u/s$inline-of-ia32e-pml4ebits-fix-x

(defthm
   !ia32e-pml4ebits->u/s$inline-of-ia32e-pml4ebits-fix-x
   (equal (!ia32e-pml4ebits->u/s$inline u/s (ia32e-pml4ebits-fix x))
          (!ia32e-pml4ebits->u/s$inline u/s x)))

Theorem: !ia32e-pml4ebits->u/s$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
  !ia32e-pml4ebits->u/s$inline-ia32e-pml4ebits-equiv-congruence-on-x
  (implies (ia32e-pml4ebits-equiv x x-equiv)
           (equal (!ia32e-pml4ebits->u/s$inline u/s x)
                  (!ia32e-pml4ebits->u/s$inline u/s x-equiv)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->u/s-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->u/s-is-ia32e-pml4ebits
        (equal (!ia32e-pml4ebits->u/s u/s x)
               (change-ia32e-pml4ebits x :u/s u/s)))

Theorem: ia32e-pml4ebits->u/s-of-!ia32e-pml4ebits->u/s

(defthm ia32e-pml4ebits->u/s-of-!ia32e-pml4ebits->u/s
        (b* ((?new-x (!ia32e-pml4ebits->u/s$inline u/s x)))
            (equal (ia32e-pml4ebits->u/s new-x)
                   (bfix u/s))))

Theorem: !ia32e-pml4ebits->u/s-equiv-under-mask

(defthm !ia32e-pml4ebits->u/s-equiv-under-mask
        (b* ((?new-x (!ia32e-pml4ebits->u/s$inline u/s x)))
            (ia32e-pml4ebits-equiv-under-mask new-x x -5)))