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Gdtr/idtrbits

Gdtr/idtrbits->base-addr

Access the |X86ISA|::|BASE-ADDR| field of a gdtr/idtrbits bit structure.

Signature
(gdtr/idtrbits->base-addr x) → base-addr
Arguments: x — Guard (gdtr/idtrbits-p x).
Returns: base-addr — Type (64bits-p base-addr).

Definitions and Theorems

Function: gdtr/idtrbits->base-addr$inline

(defun gdtr/idtrbits->base-addr$inline (x)
  (declare (xargs :guard (gdtr/idtrbits-p x)))
  (mbe :logic
       (let ((x (gdtr/idtrbits-fix x)))
         (part-select x :low 0 :width 64))
       :exec (the (unsigned-byte 64)
                  (logand (the (unsigned-byte 64)
                               18446744073709551615)
                          (the (unsigned-byte 80) x)))))

Theorem: 64bits-p-of-gdtr/idtrbits->base-addr

(defthm 64bits-p-of-gdtr/idtrbits->base-addr
  (b* ((base-addr (gdtr/idtrbits->base-addr$inline x)))
    (64bits-p base-addr))
  :rule-classes :rewrite)

Theorem: gdtr/idtrbits->base-addr$inline-of-gdtr/idtrbits-fix-x

(defthm gdtr/idtrbits->base-addr$inline-of-gdtr/idtrbits-fix-x
  (equal (gdtr/idtrbits->base-addr$inline (gdtr/idtrbits-fix x))
         (gdtr/idtrbits->base-addr$inline x)))

Theorem: gdtr/idtrbits->base-addr$inline-gdtr/idtrbits-equiv-congruence-on-x

(defthm
 gdtr/idtrbits->base-addr$inline-gdtr/idtrbits-equiv-congruence-on-x
 (implies (gdtr/idtrbits-equiv x x-equiv)
          (equal (gdtr/idtrbits->base-addr$inline x)
                 (gdtr/idtrbits->base-addr$inline x-equiv)))
 :rule-classes :congruence)

Theorem: gdtr/idtrbits->base-addr-of-gdtr/idtrbits

(defthm gdtr/idtrbits->base-addr-of-gdtr/idtrbits
  (equal (gdtr/idtrbits->base-addr (gdtr/idtrbits base-addr limit))
         (64bits-fix base-addr)))

Theorem: gdtr/idtrbits->base-addr-of-write-with-mask

(defthm gdtr/idtrbits->base-addr-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x gdtr/idtrbits-equiv-under-mask)
                (gdtr/idtrbits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask)
                               18446744073709551615)
                       0))
           (equal (gdtr/idtrbits->base-addr x)
                  (gdtr/idtrbits->base-addr y))))