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

Bip32-path-set-closedp-exec-outer

Signature

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

Arguments

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

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

Returns

yes/no — Type (booleanp yes/no).

Definitions and Theorems

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

(defun bip32-path-set-closedp-exec-outer (cur-paths all-paths)
  (declare (xargs :guard (and (bip32-path-setp cur-paths)
                              (bip32-path-setp all-paths))))
  (or (not (mbt (bip32-path-setp cur-paths)))
      (emptyp cur-paths)
      (and (bip32-path-set-closedp-exec-inner (head cur-paths)
                                              all-paths)
           (bip32-path-set-closedp-exec-outer (tail cur-paths)
                                              all-paths))))

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

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

Theorem: bip32-path-set-closedp-exec-outer-of-bip32-path-sfix-cur-paths

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

Theorem: bip32-path-set-closedp-exec-outer-bip32-path-set-equiv-congruence-on-cur-paths

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

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

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

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

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