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Vex3-byte2

!vex3-byte2->l

Update the |ACL2|::|L| field of a vex3-byte2 bit structure.

Signature
(!vex3-byte2->l l x) → new-x
Arguments: l — Guard (bitp l).; x — Guard (vex3-byte2-p x).
Returns: new-x — Type (vex3-byte2-p new-x).

Definitions and Theorems

Function: !vex3-byte2->l$inline

(defun !vex3-byte2->l$inline (l x)
 (declare (xargs :guard (and (bitp l) (vex3-byte2-p x))))
 (mbe :logic
      (b* ((l (mbe :logic (bfix l) :exec l))
           (x (vex3-byte2-fix x)))
        (part-install l x :width 1 :low 2))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 4) -5)))
                         (the (unsigned-byte 3)
                              (ash (the (unsigned-byte 1) l) 2))))))

Theorem: vex3-byte2-p-of-!vex3-byte2->l

(defthm vex3-byte2-p-of-!vex3-byte2->l
  (b* ((new-x (!vex3-byte2->l$inline l x)))
    (vex3-byte2-p new-x))
  :rule-classes :rewrite)

Theorem: !vex3-byte2->l$inline-of-bfix-l

(defthm !vex3-byte2->l$inline-of-bfix-l
  (equal (!vex3-byte2->l$inline (bfix l) x)
         (!vex3-byte2->l$inline l x)))

Theorem: !vex3-byte2->l$inline-bit-equiv-congruence-on-l

(defthm !vex3-byte2->l$inline-bit-equiv-congruence-on-l
  (implies (bit-equiv l l-equiv)
           (equal (!vex3-byte2->l$inline l x)
                  (!vex3-byte2->l$inline l-equiv x)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->l$inline-of-vex3-byte2-fix-x

(defthm !vex3-byte2->l$inline-of-vex3-byte2-fix-x
  (equal (!vex3-byte2->l$inline l (vex3-byte2-fix x))
         (!vex3-byte2->l$inline l x)))

Theorem: !vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x

(defthm !vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (!vex3-byte2->l$inline l x)
                  (!vex3-byte2->l$inline l x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->l-is-vex3-byte2

(defthm !vex3-byte2->l-is-vex3-byte2
  (equal (!vex3-byte2->l l x)
         (change-vex3-byte2 x :l l)))

Theorem: vex3-byte2->l-of-!vex3-byte2->l

(defthm vex3-byte2->l-of-!vex3-byte2->l
  (b* ((?new-x (!vex3-byte2->l$inline l x)))
    (equal (vex3-byte2->l new-x) (bfix l))))

Theorem: !vex3-byte2->l-equiv-under-mask

(defthm !vex3-byte2->l-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->l$inline l x)))
    (vex3-byte2-equiv-under-mask new-x x -5)))