		Search-engine friendly clone of the ACL2 documentation.

S4vecs

S4vec-rsh

Signature
(s4vec-rsh amt x) → res
Arguments: amt — Guard (s4vec-p amt).; x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-rsh

(defun s4vec-rsh (amt x)
  (declare (xargs :guard (and (s4vec-p amt) (s4vec-p x))))
  (let ((__function__ 's4vec-rsh))
    (declare (ignorable __function__))
    (b* (((unless (s4vec-2vec-p amt)) (s4vec-x))
         (amtval (s4vec-sparseint-val
                      (sparseint-unary-minus (s4vec->upper amt)))))
      (s4vec-shift-core amtval x))))

Theorem: s4vec-p-of-s4vec-rsh

(defthm s4vec-p-of-s4vec-rsh
  (b* ((res (s4vec-rsh amt x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-rsh-correct

(defthm s4vec-rsh-correct
  (b* ((?res (s4vec-rsh amt x)))
    (equal (s4vec->4vec res)
           (4vec-rsh (s4vec->4vec amt)
                     (s4vec->4vec x)))))

Theorem: s4vec-rsh-of-s4vec-fix-amt

(defthm s4vec-rsh-of-s4vec-fix-amt
  (equal (s4vec-rsh (s4vec-fix amt) x)
         (s4vec-rsh amt x)))

Theorem: s4vec-rsh-s4vec-equiv-congruence-on-amt

(defthm s4vec-rsh-s4vec-equiv-congruence-on-amt
  (implies (s4vec-equiv amt amt-equiv)
           (equal (s4vec-rsh amt x)
                  (s4vec-rsh amt-equiv x)))
  :rule-classes :congruence)

Theorem: s4vec-rsh-of-s4vec-fix-x

(defthm s4vec-rsh-of-s4vec-fix-x
  (equal (s4vec-rsh amt (s4vec-fix x))
         (s4vec-rsh amt x)))

Theorem: s4vec-rsh-s4vec-equiv-congruence-on-x

(defthm s4vec-rsh-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-rsh amt x)
                  (s4vec-rsh amt x-equiv)))
  :rule-classes :congruence)