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S4vecs

S4vec->upper

Signature
(s4vec->upper x) → upper
Arguments: x — Guard (s4vec-p x).
Returns: upper — Type (sparseint-p upper).

Definitions and Theorems

Function: s4vec->upper

(defun s4vec->upper (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec->upper))
    (declare (ignorable __function__))
    (if (atom x)
        (mbe :logic (if (integerp x) x -1)
             :exec x)
      (sparseint-fix (car x)))))

Theorem: sparseint-p-of-s4vec->upper

(defthm sparseint-p-of-s4vec->upper
  (b* ((upper (s4vec->upper x)))
    (sparseint-p upper))
  :rule-classes :rewrite)

Theorem: s4vec->upper-of-s4vec-fix-x

(defthm s4vec->upper-of-s4vec-fix-x
  (equal (s4vec->upper (s4vec-fix x))
         (s4vec->upper x)))

Theorem: s4vec->upper-s4vec-equiv-congruence-on-x

(defthm s4vec->upper-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec->upper x)
                  (s4vec->upper x-equiv)))
  :rule-classes :congruence)