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Cr4bits

!cr4bits->umip

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

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

Definitions and Theorems

Function: !cr4bits->umip$inline

(defun !cr4bits->umip$inline (umip x)
 (declare (xargs :guard (and (bitp umip) (cr4bits-p x))))
 (mbe :logic
      (b* ((umip (mbe :logic (bfix umip) :exec umip))
           (x (cr4bits-fix x)))
        (part-install umip x :width 1 :low 11))
      :exec (the (unsigned-byte 26)
                 (logior (the (unsigned-byte 26)
                              (logand (the (unsigned-byte 26) x)
                                      (the (signed-byte 13) -2049)))
                         (the (unsigned-byte 12)
                              (ash (the (unsigned-byte 1) umip)
                                   11))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->umip-is-cr4bits

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

Theorem: cr4bits->umip-of-!cr4bits->umip

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

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

(defthm !cr4bits->umip-equiv-under-mask
  (b* ((?new-x (!cr4bits->umip$inline umip x)))
    (cr4bits-equiv-under-mask new-x x -2049)))