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Secp256k1-field

Secp256k1-fieldp

Recognizer for secp256k1-field.

Signature
(secp256k1-fieldp x) → yes/no
Returns: yes/no — Type (booleanp yes/no).

Definitions and Theorems

Function: secp256k1-fieldp

(defun secp256k1-fieldp (x)
  (declare (xargs :guard t))
  (integer-range-p 0 (secp256k1-field-prime)
                   x))

Theorem: booleanp-of-secp256k1-fieldp

(defthm booleanp-of-secp256k1-fieldp
  (b* ((yes/no (secp256k1-fieldp x)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: natp-and-below-prime-when-secp256k1-fieldp

(defthm natp-and-below-prime-when-secp256k1-fieldp
 (implies
  (secp256k1-fieldp x)
  (and
   (natp x)
   (<
    x
    115792089237316195423570985008687907853269984665640564039457584007908834671663)))
 :rule-classes :tau-system)