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17bits

17bits-fix

Fixing function for 17bits bit structures.

Signature
(17bits-fix x) → fty::fixed
Arguments: x — Guard (17bits-p x).
Returns: fty::fixed — Type (17bits-p fty::fixed).

Definitions and Theorems

Function: 17bits-fix

(defun 17bits-fix (x)
  (declare (xargs :guard (17bits-p x)))
  (let ((__function__ '17bits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 17 x) :exec x)))

Theorem: 17bits-p-of-17bits-fix

(defthm 17bits-p-of-17bits-fix
  (b* ((fty::fixed (17bits-fix x)))
    (17bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: 17bits-fix-when-17bits-p

(defthm 17bits-fix-when-17bits-p
  (implies (17bits-p x)
           (equal (17bits-fix x) x)))

Function: 17bits-equiv$inline

(defun 17bits-equiv$inline (x y)
  (declare (xargs :guard (and (17bits-p x) (17bits-p y))))
  (equal (17bits-fix x) (17bits-fix y)))

Theorem: 17bits-equiv-is-an-equivalence

(defthm 17bits-equiv-is-an-equivalence
  (and (booleanp (17bits-equiv x y))
       (17bits-equiv x x)
       (implies (17bits-equiv x y)
                (17bits-equiv y x))
       (implies (and (17bits-equiv x y)
                     (17bits-equiv y z))
                (17bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 17bits-equiv-implies-equal-17bits-fix-1

(defthm 17bits-equiv-implies-equal-17bits-fix-1
  (implies (17bits-equiv x x-equiv)
           (equal (17bits-fix x)
                  (17bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 17bits-fix-under-17bits-equiv

(defthm 17bits-fix-under-17bits-equiv
  (17bits-equiv (17bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))