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S4vecs

S3vec-fix

Signature
(s3vec-fix x) → fix
Arguments: x — Guard (s4vec-p x).
Returns: fix — Type (s4vec-p fix).

Definitions and Theorems

Function: s3vec-fix

(defun s3vec-fix (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's3vec-fix))
    (declare (ignorable __function__))
    (b* (((s4vec x)))
      (if (s3vec-p x)
          (s4vec-fix x)
        (s4vec (sparseint-bitor x.upper x.lower)
               (sparseint-bitand x.upper x.lower))))))

Theorem: s4vec-p-of-s3vec-fix

(defthm s4vec-p-of-s3vec-fix
  (b* ((fix (s3vec-fix x))) (s4vec-p fix))
  :rule-classes :rewrite)

Theorem: s3vec-fix-correct

(defthm s3vec-fix-correct
  (b* ((acl2::?fix (s3vec-fix x)))
    (equal (s4vec->4vec fix)
           (3vec-fix (s4vec->4vec x)))))

Theorem: s3vec-fix-of-s4vec-fix-x

(defthm s3vec-fix-of-s4vec-fix-x
  (equal (s3vec-fix (s4vec-fix x))
         (s3vec-fix x)))

Theorem: s3vec-fix-s4vec-equiv-congruence-on-x

(defthm s3vec-fix-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s3vec-fix x)
                  (s3vec-fix x-equiv)))
  :rule-classes :congruence)