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Rewriting

Svex-mask-alist-keys

Signature
(svex-mask-alist-keys x) → keys
Arguments: x — Guard (svex-mask-alist-p x).
Returns: keys — Type (svexlist-p keys).

Definitions and Theorems

Function: svex-mask-alist-keys

(defun svex-mask-alist-keys (x)
  (declare (xargs :guard (svex-mask-alist-p x)))
  (let ((__function__ 'svex-mask-alist-keys))
    (declare (ignorable __function__))
    (if (atom x)
        nil
      (if (mbt (and (consp (car x)) (svex-p (caar x))))
          (cons (caar x)
                (svex-mask-alist-keys (cdr x)))
        (svex-mask-alist-keys (cdr x))))))

Theorem: svexlist-p-of-svex-mask-alist-keys

(defthm svexlist-p-of-svex-mask-alist-keys
  (b* ((keys (svex-mask-alist-keys x)))
    (svexlist-p keys))
  :rule-classes :rewrite)

Theorem: svex-mask-alist-keys-of-svex-mask-alist-fix-x

(defthm svex-mask-alist-keys-of-svex-mask-alist-fix-x
  (equal (svex-mask-alist-keys (svex-mask-alist-fix x))
         (svex-mask-alist-keys x)))

Theorem: svex-mask-alist-keys-svex-mask-alist-equiv-congruence-on-x

(defthm svex-mask-alist-keys-svex-mask-alist-equiv-congruence-on-x
  (implies (svex-mask-alist-equiv x x-equiv)
           (equal (svex-mask-alist-keys x)
                  (svex-mask-alist-keys x-equiv)))
  :rule-classes :congruence)

Theorem: member-svex-mask-alist-keys

(defthm member-svex-mask-alist-keys
  (implies (not (member (svex-fix k)
                        (svex-mask-alist-keys x)))
           (equal (svex-mask-lookup k x) 0)))

Theorem: svex-mask-alist-keys-of-svex-mask-acons

(defthm svex-mask-alist-keys-of-svex-mask-acons
  (equal (svex-mask-alist-keys (svex-mask-acons k v x))
         (cons (svex-fix k)
               (svex-mask-alist-keys x))))