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• Bip44

Bip44-compliant-addresses-p

Check if the address keys under a given chain key in a tree comply with the BIP 44 wallet structure.

This is obtained by existentially quantifying the address index limit in bip44-compliant-addresses-for-limit-p. See the documentation of that function for details.

[BIP44] states that the address keys are not hardened, so we require the limit to be at most 2^{31}.

Definitions and Theorems

Theorem: bip44-compliant-addresses-p-suff

(defthm bip44-compliant-addresses-p-suff
  (implies (and (natp address-index-limit)
                (<= address-index-limit (expt 2 31))
                (bip44-compliant-addresses-for-limit-p
                     tree coin-index account-index
                     chain-index address-index-limit))
           (bip44-compliant-addresses-p
                tree
                coin-index account-index chain-index)))

Theorem: booleanp-of-bip44-compliant-addresses-p

(defthm booleanp-of-bip44-compliant-addresses-p
  (b* ((yes/no (bip44-compliant-addresses-p
                    tree
                    coin-index account-index chain-index)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bip44-compliant-addresses-p-of-bip32-key-tree-fix-tree

(defthm bip44-compliant-addresses-p-of-bip32-key-tree-fix-tree
 (equal
  (bip44-compliant-addresses-p (bip32-key-tree-fix tree)
                               coin-index account-index chain-index)
  (bip44-compliant-addresses-p
       tree
       coin-index account-index chain-index)))

Theorem: bip44-compliant-addresses-p-bip32-key-tree-equiv-congruence-on-tree

(defthm
 bip44-compliant-addresses-p-bip32-key-tree-equiv-congruence-on-tree
 (implies (bip32-key-tree-equiv tree tree-equiv)
          (equal (bip44-compliant-addresses-p
                      tree
                      coin-index account-index chain-index)
                 (bip44-compliant-addresses-p
                      tree-equiv
                      coin-index account-index chain-index)))
 :rule-classes :congruence)

Theorem: bip44-compliant-addresses-p-of-ubyte32-fix-coin-index

(defthm bip44-compliant-addresses-p-of-ubyte32-fix-coin-index
  (equal (bip44-compliant-addresses-p tree (ubyte32-fix coin-index)
                                      account-index chain-index)
         (bip44-compliant-addresses-p
              tree
              coin-index account-index chain-index)))

Theorem: bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-coin-index

(defthm
 bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-coin-index
 (implies
    (acl2::ubyte32-equiv coin-index coin-index-equiv)
    (equal (bip44-compliant-addresses-p
                tree
                coin-index account-index chain-index)
           (bip44-compliant-addresses-p tree coin-index-equiv
                                        account-index chain-index)))
 :rule-classes :congruence)

Theorem: bip44-compliant-addresses-p-of-ubyte32-fix-account-index

(defthm bip44-compliant-addresses-p-of-ubyte32-fix-account-index
  (equal (bip44-compliant-addresses-p
              tree
              coin-index (ubyte32-fix account-index)
              chain-index)
         (bip44-compliant-addresses-p
              tree
              coin-index account-index chain-index)))

Theorem: bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-account-index

(defthm
 bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-account-index
 (implies
  (acl2::ubyte32-equiv account-index account-index-equiv)
  (equal
     (bip44-compliant-addresses-p
          tree
          coin-index account-index chain-index)
     (bip44-compliant-addresses-p tree coin-index
                                  account-index-equiv chain-index)))
 :rule-classes :congruence)

Theorem: bip44-compliant-addresses-p-of-ubyte32-fix-chain-index

(defthm bip44-compliant-addresses-p-of-ubyte32-fix-chain-index
  (equal (bip44-compliant-addresses-p
              tree coin-index
              account-index (ubyte32-fix chain-index))
         (bip44-compliant-addresses-p
              tree
              coin-index account-index chain-index)))

Theorem: bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-chain-index

(defthm
 bip44-compliant-addresses-p-ubyte32-equiv-congruence-on-chain-index
 (implies
  (acl2::ubyte32-equiv chain-index chain-index-equiv)
  (equal
     (bip44-compliant-addresses-p
          tree
          coin-index account-index chain-index)
     (bip44-compliant-addresses-p tree coin-index
                                  account-index chain-index-equiv)))
 :rule-classes :congruence)