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Modalist

Modalist-addr-p

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

Definitions and Theorems

Function: modalist-addr-p

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

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

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

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

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