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S4vecs

S4vec->lower

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

Definitions and Theorems

Function: s4vec->lower

(defun s4vec->lower (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec->lower))
    (declare (ignorable __function__))
    (if (atom x)
        (lifix x)
      (if (cdr x)
          (sparseint-fix (cdr x))
        (sparseint-fix (car x))))))

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

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

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

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

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

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