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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))