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• Bip32-path-set-closedp-executable-attachment

Bip32-path-set-closedp-exec-inner

Signature

(bip32-path-set-closedp-exec-inner cur-path all-paths) 
  → 
yes/no

Arguments

cur-path — Guard (ubyte32-listp cur-path).

all-paths — Guard (bip32-path-setp all-paths).

Returns

yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: bip32-path-set-closedp-exec-inner

(defun bip32-path-set-closedp-exec-inner (cur-path all-paths)
  (declare (xargs :guard (and (ubyte32-listp cur-path)
                              (bip32-path-setp all-paths))))
  (and (in (ubyte32-list-fix cur-path)
           (bip32-path-sfix all-paths))
       (or (endp cur-path)
           (bip32-path-set-closedp-exec-inner (butlast cur-path 1)
                                              all-paths))))

Theorem: booleanp-of-bip32-path-set-closedp-exec-inner

(defthm booleanp-of-bip32-path-set-closedp-exec-inner
  (b*
   ((yes/no (bip32-path-set-closedp-exec-inner cur-path all-paths)))
   (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bip32-path-set-closedp-exec-inner-of-ubyte32-list-fix-cur-path

(defthm
     bip32-path-set-closedp-exec-inner-of-ubyte32-list-fix-cur-path
 (equal
      (bip32-path-set-closedp-exec-inner (ubyte32-list-fix cur-path)
                                         all-paths)
      (bip32-path-set-closedp-exec-inner cur-path all-paths)))

Theorem: bip32-path-set-closedp-exec-inner-ubyte32-list-equiv-congruence-on-cur-path

(defthm
 bip32-path-set-closedp-exec-inner-ubyte32-list-equiv-congruence-on-cur-path
 (implies
  (acl2::ubyte32-list-equiv cur-path cur-path-equiv)
  (equal
      (bip32-path-set-closedp-exec-inner cur-path all-paths)
      (bip32-path-set-closedp-exec-inner cur-path-equiv all-paths)))
 :rule-classes :congruence)

Theorem: bip32-path-set-closedp-exec-inner-of-bip32-path-sfix-all-paths

(defthm
     bip32-path-set-closedp-exec-inner-of-bip32-path-sfix-all-paths
  (equal (bip32-path-set-closedp-exec-inner
              cur-path (bip32-path-sfix all-paths))
         (bip32-path-set-closedp-exec-inner cur-path all-paths)))

Theorem: bip32-path-set-closedp-exec-inner-bip32-path-set-equiv-congruence-on-all-paths

(defthm
 bip32-path-set-closedp-exec-inner-bip32-path-set-equiv-congruence-on-all-paths
 (implies
  (bip32-path-set-equiv all-paths all-paths-equiv)
  (equal
      (bip32-path-set-closedp-exec-inner cur-path all-paths)
      (bip32-path-set-closedp-exec-inner cur-path all-paths-equiv)))
 :rule-classes :congruence)