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Cr8bits

!cr8bits->cr8-trpl

Update the |X86ISA|::|CR8-TRPL| field of a cr8bits bit structure.

Signature
(!cr8bits->cr8-trpl cr8-trpl x) → new-x
Arguments: cr8-trpl — Guard (4bits-p cr8-trpl).; x — Guard (cr8bits-p x).
Returns: new-x — Type (cr8bits-p new-x).

Definitions and Theorems

Function: !cr8bits->cr8-trpl$inline

(defun !cr8bits->cr8-trpl$inline (cr8-trpl x)
  (declare (xargs :guard (and (4bits-p cr8-trpl) (cr8bits-p x))))
  (mbe :logic
       (b* ((cr8-trpl (mbe :logic (4bits-fix cr8-trpl)
                           :exec cr8-trpl))
            (x (cr8bits-fix x)))
         (part-install cr8-trpl x
                       :width 4
                       :low 0))
       :exec (the (unsigned-byte 4)
                  (logior (the (unsigned-byte 4)
                               (logand (the (unsigned-byte 4) x)
                                       (the (signed-byte 5) -16)))
                          (the (unsigned-byte 4) cr8-trpl)))))

Theorem: cr8bits-p-of-!cr8bits->cr8-trpl

(defthm cr8bits-p-of-!cr8bits->cr8-trpl
  (b* ((new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (cr8bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr8bits->cr8-trpl$inline-of-4bits-fix-cr8-trpl

(defthm !cr8bits->cr8-trpl$inline-of-4bits-fix-cr8-trpl
  (equal (!cr8bits->cr8-trpl$inline (4bits-fix cr8-trpl)
                                    x)
         (!cr8bits->cr8-trpl$inline cr8-trpl x)))

Theorem: !cr8bits->cr8-trpl$inline-4bits-equiv-congruence-on-cr8-trpl

(defthm !cr8bits->cr8-trpl$inline-4bits-equiv-congruence-on-cr8-trpl
  (implies (4bits-equiv cr8-trpl cr8-trpl-equiv)
           (equal (!cr8bits->cr8-trpl$inline cr8-trpl x)
                  (!cr8bits->cr8-trpl$inline cr8-trpl-equiv x)))
  :rule-classes :congruence)

Theorem: !cr8bits->cr8-trpl$inline-of-cr8bits-fix-x

(defthm !cr8bits->cr8-trpl$inline-of-cr8bits-fix-x
  (equal (!cr8bits->cr8-trpl$inline cr8-trpl (cr8bits-fix x))
         (!cr8bits->cr8-trpl$inline cr8-trpl x)))

Theorem: !cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x

(defthm !cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x
  (implies (cr8bits-equiv x x-equiv)
           (equal (!cr8bits->cr8-trpl$inline cr8-trpl x)
                  (!cr8bits->cr8-trpl$inline cr8-trpl x-equiv)))
  :rule-classes :congruence)

Theorem: !cr8bits->cr8-trpl-is-cr8bits

(defthm !cr8bits->cr8-trpl-is-cr8bits
  (equal (!cr8bits->cr8-trpl cr8-trpl x)
         (change-cr8bits x :cr8-trpl cr8-trpl)))

Theorem: cr8bits->cr8-trpl-of-!cr8bits->cr8-trpl

(defthm cr8bits->cr8-trpl-of-!cr8bits->cr8-trpl
  (b* ((?new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (equal (cr8bits->cr8-trpl new-x)
           (4bits-fix cr8-trpl))))

Theorem: !cr8bits->cr8-trpl-equiv-under-mask

(defthm !cr8bits->cr8-trpl-equiv-under-mask
  (b* ((?new-x (!cr8bits->cr8-trpl$inline cr8-trpl x)))
    (cr8bits-equiv-under-mask new-x x 0)))