		Search-engine friendly clone of the ACL2 documentation.

S4vecs

S4vec-reduction-and

Signature
(s4vec-reduction-and x) → res
Arguments: x — Guard (s4vec-p x).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-reduction-and

(defun s4vec-reduction-and (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec-reduction-and))
    (declare (ignorable __function__))
    (s3vec-reduction-and (s3vec-fix x))))

Theorem: s4vec-p-of-s4vec-reduction-and

(defthm s4vec-p-of-s4vec-reduction-and
  (b* ((res (s4vec-reduction-and x)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-reduction-and-correct

(defthm s4vec-reduction-and-correct
  (b* ((?res (s4vec-reduction-and x)))
    (equal (s4vec->4vec res)
           (4vec-reduction-and (s4vec->4vec x)))))

Theorem: s4vec-reduction-and-of-s4vec-fix-x

(defthm s4vec-reduction-and-of-s4vec-fix-x
  (equal (s4vec-reduction-and (s4vec-fix x))
         (s4vec-reduction-and x)))

Theorem: s4vec-reduction-and-s4vec-equiv-congruence-on-x

(defthm s4vec-reduction-and-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-reduction-and x)
                  (s4vec-reduction-and x-equiv)))
  :rule-classes :congruence)