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Twisted-edwards-curve

Twisted-edwards-curve->d

Get the d field from a twisted-edwards-curve.

Signature
(twisted-edwards-curve->d x) → fty::x.name
Arguments: x — Guard (twisted-edwards-curvep x).

This is an ordinary field accessor created by fty::defprod.

Definitions and Theorems

Function: twisted-edwards-curve->d$inline

(defun twisted-edwards-curve->d$inline (x)
  (declare (xargs :guard (twisted-edwards-curvep x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'twisted-edwards-curve->d))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((x (and t x))
              (p (nfix (cdr (std::da-nth 0 x))))
              (a (cdr (std::da-nth 1 x)))
              (d (cdr (std::da-nth 2 x))))
           (if (and (dm::primep p)
                    (> p 2)
                    (fep a p)
                    (fep d p)
                    (not (equal a d))
                    (not (equal a 0))
                    (not (equal d 0)))
               d
             2))
         :exec (cdr (std::da-nth 2 x)))))

Theorem: twisted-edwards-curve->d$inline-of-twisted-edwards-curve-fix-x

(defthm
     twisted-edwards-curve->d$inline-of-twisted-edwards-curve-fix-x
 (equal
     (twisted-edwards-curve->d$inline (twisted-edwards-curve-fix x))
     (twisted-edwards-curve->d$inline x)))

Theorem: twisted-edwards-curve->d$inline-twisted-edwards-curve-equiv-congruence-on-x

(defthm
 twisted-edwards-curve->d$inline-twisted-edwards-curve-equiv-congruence-on-x
 (implies (twisted-edwards-curve-equiv x x-equiv)
          (equal (twisted-edwards-curve->d$inline x)
                 (twisted-edwards-curve->d$inline x-equiv)))
 :rule-classes :congruence)