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Npn4

Npn4-fix

Fixing function for npn4 bit structures.

Signature
(npn4-fix x) → fty::fixed
Arguments: x — Guard (npn4-p x).
Returns: fty::fixed — Type (npn4-p fty::fixed).

Definitions and Theorems

Function: npn4-fix

(defun npn4-fix (x)
 (declare (xargs :guard (npn4-p x)))
 (let ((__function__ 'npn4-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (loghead
    27
    (logapp
       16 (part-select x :width 16 :low 0)
       (logapp
            1 (part-select x :width 1 :low 16)
            (logapp 4 (part-select x :width 4 :low 17)
                    (perm4-fix (part-select x :width 6 :low 21))))))
   :exec x)))

Theorem: npn4-p-of-npn4-fix

(defthm npn4-p-of-npn4-fix
  (b* ((fty::fixed (npn4-fix x)))
    (npn4-p fty::fixed))
  :rule-classes :rewrite)

Theorem: npn4-fix-when-npn4-p

(defthm npn4-fix-when-npn4-p
  (implies (npn4-p x)
           (equal (npn4-fix x) x)))

Function: npn4-equiv$inline

(defun npn4-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (npn4-p acl2::x)
                              (npn4-p acl2::y))))
  (equal (npn4-fix acl2::x)
         (npn4-fix acl2::y)))

Theorem: npn4-equiv-is-an-equivalence

(defthm npn4-equiv-is-an-equivalence
  (and (booleanp (npn4-equiv x y))
       (npn4-equiv x x)
       (implies (npn4-equiv x y)
                (npn4-equiv y x))
       (implies (and (npn4-equiv x y) (npn4-equiv y z))
                (npn4-equiv x z)))
  :rule-classes (:equivalence))

Theorem: npn4-equiv-implies-equal-npn4-fix-1

(defthm npn4-equiv-implies-equal-npn4-fix-1
  (implies (npn4-equiv acl2::x x-equiv)
           (equal (npn4-fix acl2::x)
                  (npn4-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: npn4-fix-under-npn4-equiv

(defthm npn4-fix-under-npn4-equiv
  (npn4-equiv (npn4-fix acl2::x) acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: npn4-fix-of-npn4-fix-x

(defthm npn4-fix-of-npn4-fix-x
  (equal (npn4-fix (npn4-fix x))
         (npn4-fix x)))

Theorem: npn4-fix-npn4-equiv-congruence-on-x

(defthm npn4-fix-npn4-equiv-congruence-on-x
  (implies (npn4-equiv x x-equiv)
           (equal (npn4-fix x) (npn4-fix x-equiv)))
  :rule-classes :congruence)