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Cr4bits

!cr4bits->la57

Update the |X86ISA|::|LA57| field of a cr4bits bit structure.

Signature
(!cr4bits->la57 la57 x) → new-x
Arguments: la57 — Guard (bitp la57).; x — Guard (cr4bits-p x).
Returns: new-x — Type (cr4bits-p new-x).

Definitions and Theorems

Function: !cr4bits->la57$inline

(defun !cr4bits->la57$inline (la57 x)
 (declare (xargs :guard (and (bitp la57) (cr4bits-p x))))
 (mbe :logic
      (b* ((la57 (mbe :logic (bfix la57) :exec la57))
           (x (cr4bits-fix x)))
        (part-install la57 x :width 1 :low 12))
      :exec (the (unsigned-byte 26)
                 (logior (the (unsigned-byte 26)
                              (logand (the (unsigned-byte 26) x)
                                      (the (signed-byte 14) -4097)))
                         (the (unsigned-byte 13)
                              (ash (the (unsigned-byte 1) la57)
                                   12))))))

Theorem: cr4bits-p-of-!cr4bits->la57

(defthm cr4bits-p-of-!cr4bits->la57
  (b* ((new-x (!cr4bits->la57$inline la57 x)))
    (cr4bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr4bits->la57$inline-of-bfix-la57

(defthm !cr4bits->la57$inline-of-bfix-la57
  (equal (!cr4bits->la57$inline (bfix la57) x)
         (!cr4bits->la57$inline la57 x)))

Theorem: !cr4bits->la57$inline-bit-equiv-congruence-on-la57

(defthm !cr4bits->la57$inline-bit-equiv-congruence-on-la57
  (implies (bit-equiv la57 la57-equiv)
           (equal (!cr4bits->la57$inline la57 x)
                  (!cr4bits->la57$inline la57-equiv x)))
  :rule-classes :congruence)

Theorem: !cr4bits->la57$inline-of-cr4bits-fix-x

(defthm !cr4bits->la57$inline-of-cr4bits-fix-x
  (equal (!cr4bits->la57$inline la57 (cr4bits-fix x))
         (!cr4bits->la57$inline la57 x)))

Theorem: !cr4bits->la57$inline-cr4bits-equiv-congruence-on-x

(defthm !cr4bits->la57$inline-cr4bits-equiv-congruence-on-x
  (implies (cr4bits-equiv x x-equiv)
           (equal (!cr4bits->la57$inline la57 x)
                  (!cr4bits->la57$inline la57 x-equiv)))
  :rule-classes :congruence)

Theorem: !cr4bits->la57-is-cr4bits

(defthm !cr4bits->la57-is-cr4bits
  (equal (!cr4bits->la57 la57 x)
         (change-cr4bits x :la57 la57)))

Theorem: cr4bits->la57-of-!cr4bits->la57

(defthm cr4bits->la57-of-!cr4bits->la57
  (b* ((?new-x (!cr4bits->la57$inline la57 x)))
    (equal (cr4bits->la57 new-x)
           (bfix la57))))

Theorem: !cr4bits->la57-equiv-under-mask

(defthm !cr4bits->la57-equiv-under-mask
  (b* ((?new-x (!cr4bits->la57$inline la57 x)))
    (cr4bits-equiv-under-mask new-x x -4097)))