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• Bip43

Bip43-key-tree-has-purpose-p

Check if a key tree includes a subtree for a given purpose.

Signature

(bip43-key-tree-has-purpose-p tree purpose) → yes/no

Arguments

tree — Guard (bip32-key-treep tree).

purpose — Guard (bip43-purposep purpose).

Returns

yes/no — Type (booleanp yes/no).

We check if the tree is rooted at the private master key and includes the singleton path with the (hardened) purpose number.

Definitions and Theorems

Function: bip43-key-tree-has-purpose-p

(defun bip43-key-tree-has-purpose-p (tree purpose)
  (declare (xargs :guard (and (bip32-key-treep tree)
                              (bip43-purposep purpose))))
  (and (bip32-key-tree-priv-p tree)
       (equal (bip32-key-tree->root-depth tree)
              0)
       (b* ((purpose-hardened (+ (bip43-purpose-fix purpose)
                                 (expt 2 31))))
         (bip32-path-in-tree-p (list purpose-hardened)
                               tree))))

Theorem: booleanp-of-bip43-key-tree-has-purpose-p

(defthm booleanp-of-bip43-key-tree-has-purpose-p
  (b* ((yes/no (bip43-key-tree-has-purpose-p tree purpose)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bip43-key-tree-has-purpose-p-of-bip32-key-tree-fix-tree

(defthm bip43-key-tree-has-purpose-p-of-bip32-key-tree-fix-tree
  (equal (bip43-key-tree-has-purpose-p (bip32-key-tree-fix tree)
                                       purpose)
         (bip43-key-tree-has-purpose-p tree purpose)))

Theorem: bip43-key-tree-has-purpose-p-bip32-key-tree-equiv-congruence-on-tree

(defthm
 bip43-key-tree-has-purpose-p-bip32-key-tree-equiv-congruence-on-tree
 (implies (bip32-key-tree-equiv tree tree-equiv)
          (equal (bip43-key-tree-has-purpose-p tree purpose)
                 (bip43-key-tree-has-purpose-p tree-equiv purpose)))
 :rule-classes :congruence)

Theorem: bip43-key-tree-has-purpose-p-of-bip43-purpose-fix-purpose

(defthm bip43-key-tree-has-purpose-p-of-bip43-purpose-fix-purpose
 (equal
     (bip43-key-tree-has-purpose-p tree (bip43-purpose-fix purpose))
     (bip43-key-tree-has-purpose-p tree purpose)))

Theorem: bip43-key-tree-has-purpose-p-bip43-purpose-equiv-congruence-on-purpose

(defthm
 bip43-key-tree-has-purpose-p-bip43-purpose-equiv-congruence-on-purpose
 (implies (bip43-purpose-equiv purpose purpose-equiv)
          (equal (bip43-key-tree-has-purpose-p tree purpose)
                 (bip43-key-tree-has-purpose-p tree purpose-equiv)))
 :rule-classes :congruence)