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4v-sexprs

4v-alist-extract

Gather up a sub-alist from some 4v environment.

Definitions and Theorems

Function: 4v-alist-extract

(defun 4v-alist-extract (keys al)
  (declare (xargs :guard t))
  (if (atom keys)
      nil
    (cons (cons (car keys)
                (4v-lookup (car keys) al))
          (4v-alist-extract (cdr keys) al))))

Theorem: alist-keys-4v-alist-extract

(defthm alist-keys-4v-alist-extract
  (equal (alist-keys (4v-alist-extract keys alist))
         (append keys nil)))

Theorem: hons-assoc-equal-4v-alist-extract

(defthm hons-assoc-equal-4v-alist-extract
  (equal (hons-assoc-equal key (4v-alist-extract keys al))
         (and (member-equal key keys)
              (cons key
                    (4v-fix (cdr (hons-assoc-equal key al)))))))

Theorem: set-equiv-implies-key-and-env-equiv-4v-alist-extract-1

(defthm set-equiv-implies-key-and-env-equiv-4v-alist-extract-1
  (implies (set-equiv keys keys-equiv)
           (key-and-env-equiv (4v-alist-extract keys al)
                              (4v-alist-extract keys-equiv al)))
  :rule-classes (:congruence))