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Twisted-edwards-curve

Twisted-edwards-curve->p

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

Signature
(twisted-edwards-curve->p x) → p
Arguments: x — Guard (twisted-edwards-curvep x).
Returns: p — Type (natp p).

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

Definitions and Theorems

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

(defun twisted-edwards-curve->p$inline (x)
  (declare (xargs :guard (twisted-edwards-curvep x)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'twisted-edwards-curve->p))
    (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)) p 3))
         :exec (cdr (std::da-nth 0 x)))))

Theorem: natp-of-twisted-edwards-curve->p

(defthm natp-of-twisted-edwards-curve->p
  (b* ((p (twisted-edwards-curve->p$inline x)))
    (natp p))
  :rule-classes :rewrite)

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

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

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

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