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Fp-statusbits

Fp-statusbits-fix

Fixing function for fp-statusbits bit structures.

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

Definitions and Theorems

Function: fp-statusbits-fix

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

Theorem: fp-statusbits-p-of-fp-statusbits-fix

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

Theorem: fp-statusbits-fix-when-fp-statusbits-p

(defthm fp-statusbits-fix-when-fp-statusbits-p
  (implies (fp-statusbits-p x)
           (equal (fp-statusbits-fix x) x)))

Function: fp-statusbits-equiv$inline

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

Theorem: fp-statusbits-equiv-is-an-equivalence

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

Theorem: fp-statusbits-equiv-implies-equal-fp-statusbits-fix-1

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

Theorem: fp-statusbits-fix-under-fp-statusbits-equiv

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