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S4vecs

S4vec-zero-ext

Signature
(s4vec-zero-ext x y) → res
Arguments: x — Guard (s4vec-p x).; y — Guard (s4vec-p y).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-zero-ext

(defun s4vec-zero-ext (x y)
 (declare (xargs :guard (and (s4vec-p x) (s4vec-p y))))
 (let ((__function__ 's4vec-zero-ext))
  (declare (ignorable __function__))
  (b* (((unless (s4vec-index-p x)) (s4vec-x))
       (xval (s4vec-sparseint-val (s4vec->upper x))))
   (if-s2vec-p (y)
               (s2vec (sparseint-concatenate xval (s2vec->val y)
                                             0))
               (b* (((s4vec y)))
                 (s4vec (sparseint-concatenate xval y.upper 0)
                        (sparseint-concatenate xval y.lower 0)))))))

Theorem: s4vec-p-of-s4vec-zero-ext

(defthm s4vec-p-of-s4vec-zero-ext
  (b* ((res (s4vec-zero-ext x y)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-zero-ext-correct

(defthm s4vec-zero-ext-correct
  (b* ((?res (s4vec-zero-ext x y)))
    (equal (s4vec->4vec res)
           (4vec-zero-ext (s4vec->4vec x)
                          (s4vec->4vec y)))))

Theorem: s4vec-zero-ext-of-s4vec-fix-x

(defthm s4vec-zero-ext-of-s4vec-fix-x
  (equal (s4vec-zero-ext (s4vec-fix x) y)
         (s4vec-zero-ext x y)))

Theorem: s4vec-zero-ext-s4vec-equiv-congruence-on-x

(defthm s4vec-zero-ext-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-zero-ext x y)
                  (s4vec-zero-ext x-equiv y)))
  :rule-classes :congruence)

Theorem: s4vec-zero-ext-of-s4vec-fix-y

(defthm s4vec-zero-ext-of-s4vec-fix-y
  (equal (s4vec-zero-ext x (s4vec-fix y))
         (s4vec-zero-ext x y)))

Theorem: s4vec-zero-ext-s4vec-equiv-congruence-on-y

(defthm s4vec-zero-ext-s4vec-equiv-congruence-on-y
  (implies (s4vec-equiv y y-equiv)
           (equal (s4vec-zero-ext x y)
                  (s4vec-zero-ext x y-equiv)))
  :rule-classes :congruence)