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• Crypto-hdwallet

All-valid-key-paths-p

Lift valid-key-path-p to sets of paths.

Signature

(all-valid-key-paths-p paths addresses) → yes/no

Arguments

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

addresses — Guard (natp addresses).

Returns

yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: all-valid-key-paths-p

(defun all-valid-key-paths-p (paths addresses)
  (declare (xargs :guard (and (bip32-path-setp paths)
                              (natp addresses))))
  (or (emptyp paths)
      (and (valid-key-path-p (head paths)
                             addresses)
           (all-valid-key-paths-p (tail paths)
                                  addresses))))

Theorem: booleanp-of-all-valid-key-paths-p

(defthm booleanp-of-all-valid-key-paths-p
  (b* ((yes/no (all-valid-key-paths-p paths addresses)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: valid-key-path-p-when-member-and-all-valid-key-paths-p

(defthm valid-key-path-p-when-member-and-all-valid-key-paths-p
  (implies (and (in path paths)
                (all-valid-key-paths-p paths addresses))
           (valid-key-path-p path addresses)))

Theorem: all-valid-key-paths-p-of-insert

(defthm all-valid-key-paths-p-of-insert
  (equal (all-valid-key-paths-p (insert path paths)
                                addresses)
         (and (valid-key-path-p path addresses)
              (all-valid-key-paths-p paths addresses))))

Theorem: all-valid-key-paths-p-of-1+-addresses

(defthm all-valid-key-paths-p-of-1+-addresses
  (implies (all-valid-key-paths-p paths addresses)
           (all-valid-key-paths-p paths (1+ addresses))))

Theorem: not-all-valid-key-paths-p-of-next-key-path

(defthm not-all-valid-key-paths-p-of-next-key-path
  (implies (all-valid-key-paths-p paths addresses)
           (not (in (rcons addresses *key-path-prefix*)
                    paths))))