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Base58-value

Base58-valuep

Recognizer for base58-value.

Signature
(base58-valuep x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: base58-valuep

(defun base58-valuep (x)
  (declare (xargs :guard t))
  (let ((__function__ 'base58-valuep))
    (declare (ignorable __function__))
    (dab-digitp 58 x)))

Theorem: booleanp-of-base58-valuep

(defthm booleanp-of-base58-valuep
  (b* ((yes/no (base58-valuep x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: natp-when-base58-valuep

(defthm natp-when-base58-valuep
  (implies (base58-valuep x) (natp x))
  :rule-classes :compound-recognizer)

Theorem: below-58-when-base58-valuep

(defthm below-58-when-base58-valuep
  (implies (base58-valuep x) (< x 58))
  :rule-classes :forward-chaining)

Theorem: base58-valuep-rewrite-dab-digitp-58

(defthm base58-valuep-rewrite-dab-digitp-58
  (equal (base58-valuep x)
         (dab-digitp 58 x)))

Theorem: dab-digitp-58-rewrite-base58-valuep

(defthm dab-digitp-58-rewrite-base58-valuep
  (equal (dab-digitp 58 x)
         (base58-valuep x)))