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Twisted-edwards-curve

Twisted-edwards-curvep

Recognizer for twisted-edwards-curve structures.

Signature
(twisted-edwards-curvep x) → *

Definitions and Theorems

Function: twisted-edwards-curvep

(defun twisted-edwards-curvep (x)
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'twisted-edwards-curvep))
    (declare (ignorable acl2::__function__))
    (and (mbe :logic (and (alistp x)
                          (equal (strip-cars x) '(p a d)))
              :exec (fty::alist-with-carsp x '(p a d)))
         (b* ((p (cdr (std::da-nth 0 x)))
              (?a (cdr (std::da-nth 1 x)))
              (?d (cdr (std::da-nth 2 x))))
           (and (natp p)
                (dm::primep p)
                (> p 2)
                (fep a p)
                (fep d p)
                (not (equal a d))
                (not (equal a 0))
                (not (equal d 0)))))))

Theorem: consp-when-twisted-edwards-curvep

(defthm consp-when-twisted-edwards-curvep
  (implies (twisted-edwards-curvep x)
           (consp x))
  :rule-classes :compound-recognizer)