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5bits

5bits-fix

Fixing function for 5bits bit structures.

Signature
(5bits-fix x) → fty::fixed
Arguments: x — Guard (5bits-p x).
Returns: fty::fixed — Type (5bits-p fty::fixed).

Definitions and Theorems

Function: 5bits-fix

(defun 5bits-fix (x)
  (declare (xargs :guard (5bits-p x)))
  (let ((__function__ '5bits-fix))
    (declare (ignorable __function__))
    (mbe :logic (loghead 5 x) :exec x)))

Theorem: 5bits-p-of-5bits-fix

(defthm 5bits-p-of-5bits-fix
  (b* ((fty::fixed (5bits-fix x)))
    (5bits-p fty::fixed))
  :rule-classes :rewrite)

Theorem: 5bits-fix-when-5bits-p

(defthm 5bits-fix-when-5bits-p
  (implies (5bits-p x)
           (equal (5bits-fix x) x)))

Function: 5bits-equiv$inline

(defun 5bits-equiv$inline (x y)
  (declare (xargs :guard (and (5bits-p x) (5bits-p y))))
  (equal (5bits-fix x) (5bits-fix y)))

Theorem: 5bits-equiv-is-an-equivalence

(defthm 5bits-equiv-is-an-equivalence
  (and (booleanp (5bits-equiv x y))
       (5bits-equiv x x)
       (implies (5bits-equiv x y)
                (5bits-equiv y x))
       (implies (and (5bits-equiv x y)
                     (5bits-equiv y z))
                (5bits-equiv x z)))
  :rule-classes (:equivalence))

Theorem: 5bits-equiv-implies-equal-5bits-fix-1

(defthm 5bits-equiv-implies-equal-5bits-fix-1
  (implies (5bits-equiv x x-equiv)
           (equal (5bits-fix x)
                  (5bits-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: 5bits-fix-under-5bits-equiv

(defthm 5bits-fix-under-5bits-equiv
  (5bits-equiv (5bits-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))