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• Nibblelist-bytelist-map

Nibblelist-bytelist-mapp

Recognizer for nibblelist-bytelist-map.

Signature

(nibblelist-bytelist-mapp x) → *

Definitions and Theorems

Function: nibblelist-bytelist-mapp

(defun nibblelist-bytelist-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (nibble-listp (caar x))
         (byte-listp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (nibblelist-bytelist-mapp (cdr x)))))))

Theorem: booleanp-of-nibblelist-bytelist-mapp

(defthm booleanp-of-nibblelist-bytelist-mapp
  (booleanp (nibblelist-bytelist-mapp x)))

Theorem: mapp-when-nibblelist-bytelist-mapp

(defthm mapp-when-nibblelist-bytelist-mapp
  (implies (nibblelist-bytelist-mapp x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: nibblelist-bytelist-mapp-of-tail

(defthm nibblelist-bytelist-mapp-of-tail
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::tail x))))

Theorem: nibble-listp-of-head-key-when-nibblelist-bytelist-mapp

(defthm nibble-listp-of-head-key-when-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (not (omap::emptyp x)))
           (nibble-listp (mv-nth 0 (omap::head x)))))

Theorem: byte-listp-of-head-val-when-nibblelist-bytelist-mapp

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

Theorem: nibblelist-bytelist-mapp-of-update

(defthm nibblelist-bytelist-mapp-of-update
  (implies (and (nibblelist-bytelist-mapp x)
                (nibble-listp k)
                (byte-listp v))
           (nibblelist-bytelist-mapp (omap::update k v x))))

Theorem: nibblelist-bytelist-mapp-of-update*

(defthm nibblelist-bytelist-mapp-of-update*
  (implies (and (nibblelist-bytelist-mapp x)
                (nibblelist-bytelist-mapp y))
           (nibblelist-bytelist-mapp (omap::update* x y))))

Theorem: nibblelist-bytelist-mapp-of-delete

(defthm nibblelist-bytelist-mapp-of-delete
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::delete k x))))

Theorem: nibblelist-bytelist-mapp-of-delete*

(defthm nibblelist-bytelist-mapp-of-delete*
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::delete* k x))))

Theorem: nibble-listp-when-assoc-nibblelist-bytelist-mapp-binds-free-x

(defthm
      nibble-listp-when-assoc-nibblelist-bytelist-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (nibblelist-bytelist-mapp x))
           (nibble-listp k)))

Theorem: nibble-listp-of-car-of-assoc-nibblelist-bytelist-mapp

(defthm nibble-listp-of-car-of-assoc-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (nibble-listp (car (omap::assoc k x)))))

Theorem: byte-listp-of-cdr-of-assoc-nibblelist-bytelist-mapp

(defthm byte-listp-of-cdr-of-assoc-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (byte-listp (cdr (omap::assoc k x)))))

Theorem: byte-listp-of-lookup-when-nibblelist-bytelist-mapp

(defthm byte-listp-of-lookup-when-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (byte-listp (omap::lookup k x))))