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• Bip32-key-trees

Bip32-ckd-pub*

Public key designated by a specified path in the tree with the specified root public key.

Signature

(bip32-ckd-pub* root path) → (mv error? key)

Arguments

root — Guard (bip32-ext-pub-key-p root).

path — Guard (ubyte32-listp path).

Returns

error? — Type (booleanp error?).

key — Type (bip32-ext-pub-key-p key).

Definitions and Theorems

Function: bip32-ckd-pub*

(defun bip32-ckd-pub* (root path)
  (declare (xargs :guard (and (bip32-ext-pub-key-p root)
                              (ubyte32-listp path))))
  (b* ((root (mbe :logic (bip32-ext-pub-key-fix root)
                  :exec root))
       ((when (endp path)) (mv nil root))
       ((mv error? next)
        (bip32-ckd-pub root (car path)))
       ((when error?) (mv t root)))
    (bip32-ckd-pub* next (cdr path))))

Theorem: booleanp-of-bip32-ckd-pub*.error?

(defthm booleanp-of-bip32-ckd-pub*.error?
  (b* (((mv ?error? ?key)
        (bip32-ckd-pub* root path)))
    (booleanp error?))
  :rule-classes :rewrite)

Theorem: bip32-ext-pub-key-p-of-bip32-ckd-pub*.key

(defthm bip32-ext-pub-key-p-of-bip32-ckd-pub*.key
  (b* (((mv ?error? ?key)
        (bip32-ckd-pub* root path)))
    (bip32-ext-pub-key-p key))
  :rule-classes :rewrite)

Theorem: bip32-ckd-pub*-of-bip32-ext-pub-key-fix-root

(defthm bip32-ckd-pub*-of-bip32-ext-pub-key-fix-root
  (equal (bip32-ckd-pub* (bip32-ext-pub-key-fix root)
                         path)
         (bip32-ckd-pub* root path)))

Theorem: bip32-ckd-pub*-bip32-ext-pub-key-equiv-congruence-on-root

(defthm bip32-ckd-pub*-bip32-ext-pub-key-equiv-congruence-on-root
  (implies (bip32-ext-pub-key-equiv root root-equiv)
           (equal (bip32-ckd-pub* root path)
                  (bip32-ckd-pub* root-equiv path)))
  :rule-classes :congruence)

Theorem: bip32-ckd-pub*-of-ubyte32-list-fix-path

(defthm bip32-ckd-pub*-of-ubyte32-list-fix-path
  (equal (bip32-ckd-pub* root (ubyte32-list-fix path))
         (bip32-ckd-pub* root path)))

Theorem: bip32-ckd-pub*-ubyte32-list-equiv-congruence-on-path

(defthm bip32-ckd-pub*-ubyte32-list-equiv-congruence-on-path
  (implies (acl2::ubyte32-list-equiv path path-equiv)
           (equal (bip32-ckd-pub* root path)
                  (bip32-ckd-pub* root path-equiv)))
  :rule-classes :congruence)