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String-stringlist-map

String-stringlist-mapp

Recognizer for string-stringlist-map.

Signature
(string-stringlist-mapp x) → *

Definitions and Theorems

Function: string-stringlist-mapp

(defun string-stringlist-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (stringp (caar x))
         (string-listp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (fast-<< (caar x) (caadr x))
                  (string-stringlist-mapp (cdr x)))))))

Theorem: booleanp-of-string-stringlist-mapp

(defthm booleanp-of-string-stringlist-mapp
  (booleanp (string-stringlist-mapp x)))

Theorem: mapp-when-string-stringlist-mapp

(defthm mapp-when-string-stringlist-mapp
  (implies (string-stringlist-mapp x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: string-stringlist-mapp-of-tail

(defthm string-stringlist-mapp-of-tail
  (implies (string-stringlist-mapp x)
           (string-stringlist-mapp (omap::tail x))))

Theorem: stringp-of-head-key-when-string-stringlist-mapp

(defthm stringp-of-head-key-when-string-stringlist-mapp
  (implies (and (string-stringlist-mapp x)
                (not (omap::emptyp x)))
           (stringp (mv-nth 0 (omap::head x)))))

Theorem: string-listp-of-head-val-when-string-stringlist-mapp

(defthm string-listp-of-head-val-when-string-stringlist-mapp
  (implies (and (string-stringlist-mapp x)
                (not (omap::emptyp x)))
           (string-listp (mv-nth 1 (omap::head x)))))

Theorem: string-stringlist-mapp-of-update

(defthm string-stringlist-mapp-of-update
  (implies (and (string-stringlist-mapp x)
                (stringp k)
                (string-listp v))
           (string-stringlist-mapp (omap::update k v x))))

Theorem: string-stringlist-mapp-of-update*

(defthm string-stringlist-mapp-of-update*
  (implies (and (string-stringlist-mapp x)
                (string-stringlist-mapp y))
           (string-stringlist-mapp (omap::update* x y))))

Theorem: string-stringlist-mapp-of-delete

(defthm string-stringlist-mapp-of-delete
  (implies (string-stringlist-mapp x)
           (string-stringlist-mapp (omap::delete k x))))

Theorem: string-stringlist-mapp-of-delete*

(defthm string-stringlist-mapp-of-delete*
  (implies (string-stringlist-mapp x)
           (string-stringlist-mapp (omap::delete* k x))))

Theorem: stringp-when-assoc-string-stringlist-mapp-binds-free-x

(defthm stringp-when-assoc-string-stringlist-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (string-stringlist-mapp x))
           (stringp k)))

Theorem: stringp-of-car-of-assoc-string-stringlist-mapp

(defthm stringp-of-car-of-assoc-string-stringlist-mapp
  (implies (and (string-stringlist-mapp x)
                (omap::assoc k x))
           (stringp (car (omap::assoc k x)))))

Theorem: string-listp-of-cdr-of-assoc-string-stringlist-mapp

(defthm string-listp-of-cdr-of-assoc-string-stringlist-mapp
  (implies (and (string-stringlist-mapp x)
                (omap::assoc k x))
           (string-listp (cdr (omap::assoc k x)))))

Theorem: string-listp-of-lookup-when-string-stringlist-mapp

(defthm string-listp-of-lookup-when-string-stringlist-mapp
  (implies (and (string-stringlist-mapp x)
                (omap::assoc k x))
           (string-listp (omap::lookup k x))))