		Search-engine friendly clone of the ACL2 documentation.

13bits

13bits-fix

Fixing function for 13bits bit structures.

Signature
(13bits-fix x) → fty::fixed
Arguments: x — Guard (13bits-p x).
Returns: fty::fixed — Type (13bits-p fty::fixed).

Definitions and Theorems

Function: 13bits-fix

(defun 13bits-fix (x)
  (declare (xargs :guard (13bits-p x)))
  (let ((__function__ '13bits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 13 x) :exec x)))

Theorem: 13bits-p-of-13bits-fix

(defthm 13bits-p-of-13bits-fix
  (b* ((fty::fixed (13bits-fix x)))
    (13bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: 13bits-fix-when-13bits-p

(defthm 13bits-fix-when-13bits-p
  (implies (13bits-p x)
           (equal (13bits-fix x) x)))

Function: 13bits-equiv$inline

(defun 13bits-equiv$inline (x y)
  (declare (xargs :guard (and (13bits-p x) (13bits-p y))))
  (equal (13bits-fix x) (13bits-fix y)))

Theorem: 13bits-equiv-is-an-equivalence

(defthm 13bits-equiv-is-an-equivalence
  (and (booleanp (13bits-equiv x y))
       (13bits-equiv x x)
       (implies (13bits-equiv x y)
                (13bits-equiv y x))
       (implies (and (13bits-equiv x y)
                     (13bits-equiv y z))
                (13bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 13bits-equiv-implies-equal-13bits-fix-1

(defthm 13bits-equiv-implies-equal-13bits-fix-1
  (implies (13bits-equiv x x-equiv)
           (equal (13bits-fix x)
                  (13bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 13bits-fix-under-13bits-equiv

(defthm 13bits-fix-under-13bits-equiv
  (13bits-equiv (13bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))