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Segment-selectorbits

Segment-selectorbits-fix

Fixing function for segment-selectorbits bit structures.

Signature
(segment-selectorbits-fix x) → fty::fixed
Arguments: x — Guard (segment-selectorbits-p x).
Returns: fty::fixed — Type (segment-selectorbits-p fty::fixed).

Definitions and Theorems

Function: segment-selectorbits-fix

(defun segment-selectorbits-fix (x)
  (declare (xargs :guard (segment-selectorbits-p x)))
  (let ((__function__ 'segment-selectorbits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 16 x) :exec x)))

Theorem: segment-selectorbits-p-of-segment-selectorbits-fix

(defthm segment-selectorbits-p-of-segment-selectorbits-fix
  (b* ((fty::fixed (segment-selectorbits-fix x)))
    (segment-selectorbits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: segment-selectorbits-fix-when-segment-selectorbits-p

(defthm segment-selectorbits-fix-when-segment-selectorbits-p
  (implies (segment-selectorbits-p x)
           (equal (segment-selectorbits-fix x) x)))

Function: segment-selectorbits-equiv$inline

(defun segment-selectorbits-equiv$inline (x y)
  (declare (xargs :guard (and (segment-selectorbits-p x)
                              (segment-selectorbits-p y))))
  (equal (segment-selectorbits-fix x)
         (segment-selectorbits-fix y)))

Theorem: segment-selectorbits-equiv-is-an-equivalence

(defthm segment-selectorbits-equiv-is-an-equivalence
  (and (booleanp (segment-selectorbits-equiv x y))
       (segment-selectorbits-equiv x x)
       (implies (segment-selectorbits-equiv x y)
                (segment-selectorbits-equiv y x))
       (implies (and (segment-selectorbits-equiv x y)
                     (segment-selectorbits-equiv y z))
                (segment-selectorbits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: segment-selectorbits-equiv-implies-equal-segment-selectorbits-fix-1

(defthm
 segment-selectorbits-equiv-implies-equal-segment-selectorbits-fix-1
 (implies (segment-selectorbits-equiv x x-equiv)
          (equal (segment-selectorbits-fix x)
                 (segment-selectorbits-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: segment-selectorbits-fix-under-segment-selectorbits-equiv

(defthm segment-selectorbits-fix-under-segment-selectorbits-equiv
  (segment-selectorbits-equiv (segment-selectorbits-fix x)
                              x)
  :rule-classes (:rewrite :rewrite-quoted-constant))