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Ia32e-pml4ebits

!ia32e-pml4ebits->pdpt

Update the |X86ISA|::|PDPT| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->pdpt pdpt x) → new-x
Arguments: pdpt — Guard (40bits-p pdpt).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->pdpt$inline

(defun !ia32e-pml4ebits->pdpt$inline (pdpt x)
  (declare (xargs :guard (and (40bits-p pdpt)
                              (ia32e-pml4ebits-p x))))
  (mbe :logic
       (b* ((pdpt (mbe :logic (40bits-fix pdpt)
                       :exec pdpt))
            (x (ia32e-pml4ebits-fix x)))
         (part-install pdpt x :width 40 :low 12))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 53)
                                            -4503599627366401)))
                          (the (unsigned-byte 52)
                               (ash (the (unsigned-byte 40) pdpt)
                                    12))))))

Theorem: ia32e-pml4ebits-p-of-!ia32e-pml4ebits->pdpt

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

Theorem: !ia32e-pml4ebits->pdpt$inline-of-40bits-fix-pdpt

(defthm !ia32e-pml4ebits->pdpt$inline-of-40bits-fix-pdpt
  (equal (!ia32e-pml4ebits->pdpt$inline (40bits-fix pdpt)
                                        x)
         (!ia32e-pml4ebits->pdpt$inline pdpt x)))

Theorem: !ia32e-pml4ebits->pdpt$inline-40bits-equiv-congruence-on-pdpt

(defthm
      !ia32e-pml4ebits->pdpt$inline-40bits-equiv-congruence-on-pdpt
  (implies (40bits-equiv pdpt pdpt-equiv)
           (equal (!ia32e-pml4ebits->pdpt$inline pdpt x)
                  (!ia32e-pml4ebits->pdpt$inline pdpt-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->pdpt$inline-of-ia32e-pml4ebits-fix-x

(defthm !ia32e-pml4ebits->pdpt$inline-of-ia32e-pml4ebits-fix-x
 (equal (!ia32e-pml4ebits->pdpt$inline pdpt (ia32e-pml4ebits-fix x))
        (!ia32e-pml4ebits->pdpt$inline pdpt x)))

Theorem: !ia32e-pml4ebits->pdpt$inline-ia32e-pml4ebits-equiv-congruence-on-x

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

Theorem: !ia32e-pml4ebits->pdpt-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->pdpt-is-ia32e-pml4ebits
  (equal (!ia32e-pml4ebits->pdpt pdpt x)
         (change-ia32e-pml4ebits x :pdpt pdpt)))

Theorem: ia32e-pml4ebits->pdpt-of-!ia32e-pml4ebits->pdpt

(defthm ia32e-pml4ebits->pdpt-of-!ia32e-pml4ebits->pdpt
  (b* ((?new-x (!ia32e-pml4ebits->pdpt$inline pdpt x)))
    (equal (ia32e-pml4ebits->pdpt new-x)
           (40bits-fix pdpt))))

Theorem: !ia32e-pml4ebits->pdpt-equiv-under-mask

(defthm !ia32e-pml4ebits->pdpt-equiv-under-mask
  (b* ((?new-x (!ia32e-pml4ebits->pdpt$inline pdpt x)))
    (ia32e-pml4ebits-equiv-under-mask new-x x -4503599627366401)))