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Validators-state

Validators-statep

Recognizer for validators-state.

Signature
(validators-statep x) → *

Definitions and Theorems

Function: validators-statep

(defun validators-statep (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (addressp (caar x))
         (validator-statep (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (validators-statep (cdr x)))))))

Theorem: booleanp-of-validators-statep

(defthm booleanp-of-validators-statep
  (booleanp (validators-statep x)))

Theorem: mapp-when-validators-statep

(defthm mapp-when-validators-statep
  (implies (validators-statep x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: validators-statep-of-tail

(defthm validators-statep-of-tail
  (implies (validators-statep x)
           (validators-statep (omap::tail x))))

Theorem: addressp-of-head-key-when-validators-statep

(defthm addressp-of-head-key-when-validators-statep
  (implies (and (validators-statep x)
                (not (omap::emptyp x)))
           (addressp (mv-nth 0 (omap::head x)))))

Theorem: validator-statep-of-head-val-when-validators-statep

(defthm validator-statep-of-head-val-when-validators-statep
  (implies (and (validators-statep x)
                (not (omap::emptyp x)))
           (validator-statep (mv-nth 1 (omap::head x)))))

Theorem: validators-statep-of-update

(defthm validators-statep-of-update
  (implies (and (validators-statep x)
                (addressp k)
                (validator-statep v))
           (validators-statep (omap::update k v x))))

Theorem: validators-statep-of-update*

(defthm validators-statep-of-update*
  (implies (and (validators-statep x)
                (validators-statep y))
           (validators-statep (omap::update* x y))))

Theorem: validators-statep-of-delete

(defthm validators-statep-of-delete
  (implies (validators-statep x)
           (validators-statep (omap::delete k x))))

Theorem: validators-statep-of-delete*

(defthm validators-statep-of-delete*
  (implies (validators-statep x)
           (validators-statep (omap::delete* k x))))

Theorem: addressp-when-assoc-validators-statep-binds-free-x

(defthm addressp-when-assoc-validators-statep-binds-free-x
  (implies (and (omap::assoc k x)
                (validators-statep x))
           (addressp k)))

Theorem: addressp-of-car-of-assoc-validators-statep

(defthm addressp-of-car-of-assoc-validators-statep
  (implies (and (validators-statep x)
                (omap::assoc k x))
           (addressp (car (omap::assoc k x)))))

Theorem: validator-statep-of-cdr-of-assoc-validators-statep

(defthm validator-statep-of-cdr-of-assoc-validators-statep
  (implies (and (validators-statep x)
                (omap::assoc k x))
           (validator-statep (cdr (omap::assoc k x)))))

Theorem: validator-statep-of-lookup-when-validators-statep

(defthm validator-statep-of-lookup-when-validators-statep
  (implies (and (validators-statep x)
                (omap::assoc k x))
           (validator-statep (omap::lookup k x))))