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S4vecs

4vec->s4vec

Signature
(4vec->s4vec x) → new-x
Arguments: x — Guard (4vec-p x).
Returns: new-x — Type (s4vec-p new-x).

Definitions and Theorems

Function: 4vec->s4vec

(defun 4vec->s4vec (x)
  (declare (xargs :guard (4vec-p x)))
  (let ((__function__ '4vec->s4vec))
    (declare (ignorable __function__))
    (if-2vec-p (x)
               (s2vec (int-to-sparseint (2vec->val x)))
               (s4vec (int-to-sparseint (4vec->upper x))
                      (int-to-sparseint (4vec->lower x))))))

Theorem: s4vec-p-of-4vec->s4vec

(defthm s4vec-p-of-4vec->s4vec
  (b* ((new-x (4vec->s4vec x)))
    (s4vec-p new-x))
  :rule-classes :rewrite)

Theorem: s4vec->4vec-of-4vec->s4vec

(defthm s4vec->4vec-of-4vec->s4vec
  (b* ((?new-x (4vec->s4vec x)))
    (equal (s4vec->4vec new-x)
           (4vec-fix x))))

Theorem: 4vec->s4vec-of-4vec-fix-x

(defthm 4vec->s4vec-of-4vec-fix-x
  (equal (4vec->s4vec (4vec-fix x))
         (4vec->s4vec x)))

Theorem: 4vec->s4vec-4vec-equiv-congruence-on-x

(defthm 4vec->s4vec-4vec-equiv-congruence-on-x
  (implies (4vec-equiv x x-equiv)
           (equal (4vec->s4vec x)
                  (4vec->s4vec x-equiv)))
  :rule-classes :congruence)