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Q-and-is-nilc2

(q-and-is-nilc2 x y) determines whether (q-and x (q-not y)) is always false.

This is like q-and-is-nil.

Definitions and Theorems

Function: q-and-is-nilc2

(defun q-and-is-nilc2 (x y)
  (declare (xargs :guard t))
  (cond ((eq x t) (eq y t))
        ((atom x) t)
        ((eq y t) t)
        ((atom y) nil)
        (t (and (q-and-is-nilc2 (qcar x) (qcar y))
                (q-and-is-nilc2 (qcdr x) (qcdr y))))))

Theorem: q-and-is-nilc2-removal

(defthm q-and-is-nilc2-removal
  (implies (and (force (ubddp x))
                (force (ubddp y)))
           (equal (q-and-is-nilc2 x y)
                  (not (q-and x (q-not y))))))