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• Bip44-coin-type-set

Bip44-coin-type-setp

Recognizer for bip44-coin-type-set.

Signature

(bip44-coin-type-setp x) → *

Definitions and Theorems

Function: bip44-coin-type-setp

(defun bip44-coin-type-setp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (bip44-coin-type-p (car x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (acl2::fast-<< (car x) (cadr x))
                  (bip44-coin-type-setp (cdr x)))))))

Theorem: booleanp-ofbip44-coin-type-setp

(defthm booleanp-ofbip44-coin-type-setp
  (booleanp (bip44-coin-type-setp x)))

Theorem: setp-when-bip44-coin-type-setp

(defthm setp-when-bip44-coin-type-setp
  (implies (bip44-coin-type-setp x)
           (setp x))
  :rule-classes (:rewrite))

Theorem: bip44-coin-type-p-of-head-when-bip44-coin-type-setp

(defthm bip44-coin-type-p-of-head-when-bip44-coin-type-setp
  (implies (bip44-coin-type-setp x)
           (equal (bip44-coin-type-p (head x))
                  (not (emptyp x)))))

Theorem: bip44-coin-type-setp-of-tail-when-bip44-coin-type-setp

(defthm bip44-coin-type-setp-of-tail-when-bip44-coin-type-setp
  (implies (bip44-coin-type-setp x)
           (bip44-coin-type-setp (tail x))))

Theorem: bip44-coin-type-setp-of-insert

(defthm bip44-coin-type-setp-of-insert
  (equal (bip44-coin-type-setp (insert a x))
         (and (bip44-coin-type-p a)
              (bip44-coin-type-setp (sfix x)))))

Theorem: bip44-coin-type-p-when-in-bip44-coin-type-setp-binds-free-x

(defthm bip44-coin-type-p-when-in-bip44-coin-type-setp-binds-free-x
  (implies (and (in a x) (bip44-coin-type-setp x))
           (bip44-coin-type-p a)))

Theorem: not-in-bip44-coin-type-setp-when-not-bip44-coin-type-p

(defthm not-in-bip44-coin-type-setp-when-not-bip44-coin-type-p
  (implies (and (bip44-coin-type-setp x)
                (not (bip44-coin-type-p a)))
           (not (in a x))))

Theorem: bip44-coin-type-setp-of-union

(defthm bip44-coin-type-setp-of-union
  (equal (bip44-coin-type-setp (union x y))
         (and (bip44-coin-type-setp (sfix x))
              (bip44-coin-type-setp (sfix y)))))

Theorem: bip44-coin-type-setp-of-intersect

(defthm bip44-coin-type-setp-of-intersect
  (implies (or (bip44-coin-type-setp x)
               (bip44-coin-type-setp y))
           (bip44-coin-type-setp (intersect x y))))

Theorem: bip44-coin-type-setp-of-difference

(defthm bip44-coin-type-setp-of-difference
  (implies (bip44-coin-type-setp x)
           (bip44-coin-type-setp (difference x y))))

Theorem: bip44-coin-type-setp-of-delete

(defthm bip44-coin-type-setp-of-delete
  (implies (bip44-coin-type-setp x)
           (bip44-coin-type-setp (delete a x))))