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S4vecs

S4vec-clog2

Signature
(s4vec-clog2 a) → res
Arguments: a — Guard (s4vec-p a).
Returns: res — Type (s4vec-p res).

Definitions and Theorems

Function: s4vec-clog2

(defun s4vec-clog2 (a)
 (declare (xargs :guard (s4vec-p a)))
 (let ((__function__ 's4vec-clog2))
  (declare (ignorable __function__))
  (if
   (s4vec-index-p a)
   (s2vec
      (int-to-sparseint
           (sparseint-length (sparseint-plus (s4vec->upper a) -1))))
   (s4vec-x))))

Theorem: s4vec-p-of-s4vec-clog2

(defthm s4vec-p-of-s4vec-clog2
  (b* ((res (s4vec-clog2 a)))
    (s4vec-p res))
  :rule-classes :rewrite)

Theorem: s4vec-clog2-correct

(defthm s4vec-clog2-correct
  (b* ((?res (s4vec-clog2 a)))
    (equal (s4vec->4vec res)
           (4vec-clog2 (s4vec->4vec a)))))

Theorem: s4vec-clog2-of-s4vec-fix-a

(defthm s4vec-clog2-of-s4vec-fix-a
  (equal (s4vec-clog2 (s4vec-fix a))
         (s4vec-clog2 a)))

Theorem: s4vec-clog2-s4vec-equiv-congruence-on-a

(defthm s4vec-clog2-s4vec-equiv-congruence-on-a
  (implies (s4vec-equiv a a-equiv)
           (equal (s4vec-clog2 a)
                  (s4vec-clog2 a-equiv)))
  :rule-classes :congruence)