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Lhspairs-addr-p

Signature
(lhspairs-addr-p x) → *
Arguments: x — Guard (lhspairs-p x).

Definitions and Theorems

Function: lhspairs-addr-p

(defun lhspairs-addr-p (x)
  (declare (xargs :guard (lhspairs-p x)))
  (let ((__function__ 'lhspairs-addr-p))
    (declare (ignorable __function__))
    (mbe :logic
         (svarlist-addr-p (lhspairs-vars x))
         :exec
         (b* ((x (lhspairs-fix x))
              ((when (atom x)) t))
           (and (lhs-addr-p (caar x))
                (lhs-addr-p (cdar x))
                (lhspairs-addr-p (cdr x)))))))

Theorem: lhspairs-addr-p-of-lhspairs-fix-x

(defthm lhspairs-addr-p-of-lhspairs-fix-x
  (equal (lhspairs-addr-p (lhspairs-fix x))
         (lhspairs-addr-p x)))

Theorem: lhspairs-addr-p-lhspairs-equiv-congruence-on-x

(defthm lhspairs-addr-p-lhspairs-equiv-congruence-on-x
  (implies (lhspairs-equiv x x-equiv)
           (equal (lhspairs-addr-p x)
                  (lhspairs-addr-p x-equiv)))
  :rule-classes :congruence)