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S4vecs

S4vec-index-p

Signature
(s4vec-index-p x) → *
Arguments: x — Guard (s4vec-p x).

Definitions and Theorems

Function: s4vec-index-p

(defun s4vec-index-p (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec-index-p))
    (declare (ignorable __function__))
    (and (s4vec-2vec-p x)
         (not (sparseint-< (s4vec->upper x) 0)))))

Theorem: s4vec-index-p-implies

(defthm s4vec-index-p-implies
  (implies (s4vec-index-p x)
           (and (equal (sparseint-val (s4vec->lower x))
                       (sparseint-val (s4vec->upper x)))
                (<= 0 (sparseint-val (s4vec->lower x)))))
  :rule-classes :forward-chaining)

Theorem: s4vec-index-p-of-s4vec-fix-x

(defthm s4vec-index-p-of-s4vec-fix-x
  (equal (s4vec-index-p (s4vec-fix x))
         (s4vec-index-p x)))

Theorem: s4vec-index-p-s4vec-equiv-congruence-on-x

(defthm s4vec-index-p-s4vec-equiv-congruence-on-x
  (implies (s4vec-equiv x x-equiv)
           (equal (s4vec-index-p x)
                  (s4vec-index-p x-equiv)))
  :rule-classes :congruence)