• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • Event-macros
      • Java
      • Bitcoin
        • Bip32
          • Bip32-wallet-structure
          • Bip32-key-trees
            • Bip32-extend-tree
            • Bip32-valid-depths-p
            • Bip32-key-tree
            • Bip32-path-set-closedp
            • Bip32-valid-keys-p
            • Bip32-index-tree
              • Bip32-index-treep
              • Bip32-index-tree-fix
            • Bip32-path-in-tree-p
            • Bip32-ckd*
            • Bip32-get-pub-key-at-path
            • Bip32-get-priv-key-at-path
            • Bip32-ckd-priv*
            • Bip32-ckd-pub*
            • Bip32-path
            • Bip32-key-tree-priv-p
            • Bip32-path-set
          • Bip32-key-serialization
          • Bip32-key-derivation
          • Bip32-executable-attachments
          • Bip32-extended-keys
          • Bip32-master-key-generation
        • Bech32
        • Bip39
        • Bip44
        • Base58
        • Bip43
        • Bytes
        • Base58check
        • Cryptography
        • Bip-350
        • Bip-173
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Bip32-index-tree

Bip32-index-treep

Recognizer for bip32-index-tree.

Signature

(bip32-index-treep x) → yes/no

Returns

yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: bip32-index-treep

(defun bip32-index-treep (x)
  (declare (xargs :guard t))
  (and (bip32-path-setp x)
       (not (emptyp x))
       (bip32-path-set-closedp x)))

Theorem: booleanp-of-bip32-index-treep

(defthm booleanp-of-bip32-index-treep
  (b* ((yes/no (bip32-index-treep x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: bip32-path-setp-when-bip32-index-treep

(defthm bip32-path-setp-when-bip32-index-treep
  (implies (bip32-index-treep x)
           (bip32-path-setp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: bip32-index-treep-of-singleton-empty-path

(defthm bip32-index-treep-of-singleton-empty-path
  (bip32-index-treep '(nil)))