		Search-engine friendly clone of the ACL2 documentation.

S4vecs

S3vec-?

Signature
(s3vec-? test then else) → res
Arguments: test — Guard (s4vec-p test).; then — Guard (s4vec-p then).; else — Guard (s4vec-p else).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s3vec-?

(defun s3vec-? (test then else)
 (declare (xargs :guard (and (s4vec-p test)
                             (s4vec-p then)
                             (s4vec-p else))))
 (let ((__function__ 's3vec-?))
  (declare (ignorable __function__))
  (b* (((s4vec test))
       ((when (sparseint-equal test.upper 0))
        (s4vec-fix else))
       ((when (not (sparseint-equal test.lower 0)))
        (s4vec-fix then))
       ((s4vec then))
       ((s4vec else)))
   (s4vec
     (sparseint-bitor (sparseint-bitor then.upper else.upper)
                      (sparseint-bitor then.lower else.lower))
     (sparseint-bitand (sparseint-bitand then.upper else.upper)
                       (sparseint-bitand then.lower else.lower))))))

Theorem: s4vec-p-of-s3vec-?

(defthm s4vec-p-of-s3vec-?
  (b* ((res (s3vec-? test then else)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s3vec-?-correct

(defthm s3vec-?-correct
  (b* ((?res (s3vec-? test then else)))
    (equal (s4vec->4vec res)
           (3vec-? (s4vec->4vec test)
                   (s4vec->4vec then)
                   (s4vec->4vec else)))))

Theorem: s3vec-?-of-s4vec-fix-test

(defthm s3vec-?-of-s4vec-fix-test
  (equal (s3vec-? (s4vec-fix test) then else)
         (s3vec-? test then else)))

Theorem: s3vec-?-s4vec-equiv-congruence-on-test

(defthm s3vec-?-s4vec-equiv-congruence-on-test
  (implies (s4vec-equiv test test-equiv)
           (equal (s3vec-? test then else)
                  (s3vec-? test-equiv then else)))
  :rule-classes :congruence)

Theorem: s3vec-?-of-s4vec-fix-then

(defthm s3vec-?-of-s4vec-fix-then
  (equal (s3vec-? test (s4vec-fix then) else)
         (s3vec-? test then else)))

Theorem: s3vec-?-s4vec-equiv-congruence-on-then

(defthm s3vec-?-s4vec-equiv-congruence-on-then
  (implies (s4vec-equiv then then-equiv)
           (equal (s3vec-? test then else)
                  (s3vec-? test then-equiv else)))
  :rule-classes :congruence)

Theorem: s3vec-?-of-s4vec-fix-else

(defthm s3vec-?-of-s4vec-fix-else
  (equal (s3vec-? test then (s4vec-fix else))
         (s3vec-? test then else)))

Theorem: s3vec-?-s4vec-equiv-congruence-on-else

(defthm s3vec-?-s4vec-equiv-congruence-on-else
  (implies (s4vec-equiv else else-equiv)
           (equal (s3vec-? test then else)
                  (s3vec-? test then else-equiv)))
  :rule-classes :congruence)