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Cutinfo

Cutinfo-fix

Fixing function for cutinfo bit structures.

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

Definitions and Theorems

Function: cutinfo-fix

(defun cutinfo-fix (x)
 (declare (xargs :guard (cutinfo-p x)))
 (let ((__function__ 'cutinfo-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (loghead
      32
      (logapp 16 (part-select x :width 16 :low 0)
              (logapp 3
                      (cutsize-fix (part-select x :width 3 :low 16))
                      (logapp 1 (part-select x :width 1 :low 19)
                              (part-select x :width 12 :low 20)))))
   :exec x)))

Theorem: cutinfo-p-of-cutinfo-fix

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

Theorem: cutinfo-fix-when-cutinfo-p

(defthm cutinfo-fix-when-cutinfo-p
  (implies (cutinfo-p x)
           (equal (cutinfo-fix x) x)))

Function: cutinfo-equiv$inline

(defun cutinfo-equiv$inline (x acl2::y)
  (declare (xargs :guard (and (cutinfo-p x)
                              (cutinfo-p acl2::y))))
  (equal (cutinfo-fix x)
         (cutinfo-fix acl2::y)))

Theorem: cutinfo-equiv-is-an-equivalence

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

Theorem: cutinfo-equiv-implies-equal-cutinfo-fix-1

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

Theorem: cutinfo-fix-under-cutinfo-equiv

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

Theorem: cutinfo-fix-of-cutinfo-fix-x

(defthm cutinfo-fix-of-cutinfo-fix-x
  (equal (cutinfo-fix (cutinfo-fix x))
         (cutinfo-fix x)))

Theorem: cutinfo-fix-cutinfo-equiv-congruence-on-x

(defthm cutinfo-fix-cutinfo-equiv-congruence-on-x
  (implies (cutinfo-equiv x x-equiv)
           (equal (cutinfo-fix x)
                  (cutinfo-fix x-equiv)))
  :rule-classes :congruence)