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Modalist

Modalist-vars

Signature
(modalist-vars x) → vars
Arguments: x — Guard (modalist-p x).
Returns: vars — Type (svarlist-p vars).

Definitions and Theorems

Function: modalist-vars

(defun modalist-vars (x)
  (declare (xargs :guard (modalist-p x)))
  (let ((__function__ 'modalist-vars))
    (declare (ignorable __function__))
    (b* ((x (modalist-fix x)))
      (if (atom x)
          nil
        (append (module-vars (cdar x))
                (modalist-vars (cdr x)))))))

Theorem: svarlist-p-of-modalist-vars

(defthm svarlist-p-of-modalist-vars
  (b* ((vars (modalist-vars x)))
    (svarlist-p vars))
  :rule-classes :rewrite)

Theorem: modalist-vars-of-append

(defthm modalist-vars-of-append
  (equal (modalist-vars (append a b))
         (append (modalist-vars a)
                 (modalist-vars b))))

Theorem: modalist-vars-of-modalist-fix-x

(defthm modalist-vars-of-modalist-fix-x
  (equal (modalist-vars (modalist-fix x))
         (modalist-vars x)))

Theorem: modalist-vars-modalist-equiv-congruence-on-x

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