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16bits

16bits-fix

Fixing function for 16bits bit structures.

Signature
(16bits-fix x) → fty::fixed
Arguments: x — Guard (16bits-p x).
Returns: fty::fixed — Type (16bits-p fty::fixed).

Definitions and Theorems

Function: 16bits-fix

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

Theorem: 16bits-p-of-16bits-fix

(defthm 16bits-p-of-16bits-fix
  (b* ((fty::fixed (16bits-fix x)))
    (16bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: 16bits-fix-when-16bits-p

(defthm 16bits-fix-when-16bits-p
  (implies (16bits-p x)
           (equal (16bits-fix x) x)))

Function: 16bits-equiv$inline

(defun 16bits-equiv$inline (x y)
  (declare (xargs :guard (and (16bits-p x) (16bits-p y))))
  (equal (16bits-fix x) (16bits-fix y)))

Theorem: 16bits-equiv-is-an-equivalence

(defthm 16bits-equiv-is-an-equivalence
  (and (booleanp (16bits-equiv x y))
       (16bits-equiv x x)
       (implies (16bits-equiv x y)
                (16bits-equiv y x))
       (implies (and (16bits-equiv x y)
                     (16bits-equiv y z))
                (16bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 16bits-equiv-implies-equal-16bits-fix-1

(defthm 16bits-equiv-implies-equal-16bits-fix-1
  (implies (16bits-equiv x x-equiv)
           (equal (16bits-fix x)
                  (16bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 16bits-fix-under-16bits-equiv

(defthm 16bits-fix-under-16bits-equiv
  (16bits-equiv (16bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))