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S4vecs

S4vec-xfree-p

Signature
(s4vec-xfree-p x) → res
Arguments: x — Guard (s4vec-p x).

Definitions and Theorems

Function: s4vec-xfree-p

(defun s4vec-xfree-p (x)
  (declare (xargs :guard (s4vec-p x)))
  (let ((__function__ 's4vec-xfree-p))
    (declare (ignorable __function__))
    (b* (((s4vec x)))
      (not (sparseint-test-bitandc2 x.upper x.lower)))))

Theorem: s4vec-xfree-p-correct

(defthm s4vec-xfree-p-correct
  (b* ((?res (s4vec-xfree-p x)))
    (equal res (4vec-xfree-p (s4vec->4vec x)))))

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

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

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

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