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Cr3bits

!cr3bits->pdb

Update the |X86ISA|::|PDB| field of a cr3bits bit structure.

Signature
(!cr3bits->pdb pdb x) → new-x
Arguments: pdb — Guard (40bits-p pdb).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->pdb$inline

(defun !cr3bits->pdb$inline (pdb x)
  (declare (xargs :guard (and (40bits-p pdb) (cr3bits-p x))))
  (mbe :logic
       (b* ((pdb (mbe :logic (40bits-fix pdb) :exec pdb))
            (x (cr3bits-fix x)))
         (part-install pdb 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) pdb)
                                    12))))))

Theorem: cr3bits-p-of-!cr3bits->pdb

(defthm cr3bits-p-of-!cr3bits->pdb
  (b* ((new-x (!cr3bits->pdb$inline pdb x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->pdb$inline-of-40bits-fix-pdb

(defthm !cr3bits->pdb$inline-of-40bits-fix-pdb
  (equal (!cr3bits->pdb$inline (40bits-fix pdb)
                               x)
         (!cr3bits->pdb$inline pdb x)))

Theorem: !cr3bits->pdb$inline-40bits-equiv-congruence-on-pdb

(defthm !cr3bits->pdb$inline-40bits-equiv-congruence-on-pdb
  (implies (40bits-equiv pdb pdb-equiv)
           (equal (!cr3bits->pdb$inline pdb x)
                  (!cr3bits->pdb$inline pdb-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->pdb$inline-of-cr3bits-fix-x

(defthm !cr3bits->pdb$inline-of-cr3bits-fix-x
  (equal (!cr3bits->pdb$inline pdb (cr3bits-fix x))
         (!cr3bits->pdb$inline pdb x)))

Theorem: !cr3bits->pdb$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->pdb$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->pdb$inline pdb x)
                  (!cr3bits->pdb$inline pdb x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->pdb-is-cr3bits

(defthm !cr3bits->pdb-is-cr3bits
  (equal (!cr3bits->pdb pdb x)
         (change-cr3bits x :pdb pdb)))

Theorem: cr3bits->pdb-of-!cr3bits->pdb

(defthm cr3bits->pdb-of-!cr3bits->pdb
  (b* ((?new-x (!cr3bits->pdb$inline pdb x)))
    (equal (cr3bits->pdb new-x)
           (40bits-fix pdb))))

Theorem: !cr3bits->pdb-equiv-under-mask

(defthm !cr3bits->pdb-equiv-under-mask
  (b* ((?new-x (!cr3bits->pdb$inline pdb x)))
    (cr3bits-equiv-under-mask new-x x -4503599627366401)))