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Svex-envlist-keyset

Signature
(svex-envlist-keyset x) → keys
Arguments: x — Guard (svex-envlist-p x).
Returns: keys — Type (and (svarlist-p keys) (setp keys)).

Definitions and Theorems

Function: svex-envlist-keyset

(defun svex-envlist-keyset (x)
  (declare (xargs :guard (svex-envlist-p x)))
  (let ((__function__ 'svex-envlist-keyset))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (union (mergesort (svarlist-filter (alist-keys (car x))))
             (svex-envlist-keyset (cdr x))))))

Theorem: return-type-of-svex-envlist-keyset

(defthm return-type-of-svex-envlist-keyset
  (b* ((keys (svex-envlist-keyset x)))
    (and (svarlist-p keys) (setp keys)))
  :rule-classes :rewrite)

Theorem: svex-envlist-keyset-sufficient

(defthm svex-envlist-keyset-sufficient
  (b* ((?keys (svex-envlist-keyset x)))
    (implies (member env x)
             (subsetp (alist-keys (svex-env-fix env))
                      keys))))

Theorem: svex-envlist-keyset-of-svex-envlist-fix-x

(defthm svex-envlist-keyset-of-svex-envlist-fix-x
  (equal (svex-envlist-keyset (svex-envlist-fix x))
         (svex-envlist-keyset x)))

Theorem: svex-envlist-keyset-svex-envlist-equiv-congruence-on-x

(defthm svex-envlist-keyset-svex-envlist-equiv-congruence-on-x
  (implies (svex-envlist-equiv x x-equiv)
           (equal (svex-envlist-keyset x)
                  (svex-envlist-keyset x-equiv)))
  :rule-classes :congruence)