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• Twisted-edwards

Twisted-edwards-point-order-leastp

Definitions and Theorems

Theorem: twisted-edwards-point-order-leastp-necc

(defthm twisted-edwards-point-order-leastp-necc
  (implies
       (twisted-edwards-point-order-leastp point order curve)
       (implies (and (natp order1)
                     (< 0 order1)
                     (< order1 (nfix order)))
                (not (equal (twisted-edwards-mul order1 point curve)
                            (twisted-edwards-zero))))))

Theorem: booleanp-of-twisted-edwards-point-order-leastp

(defthm booleanp-of-twisted-edwards-point-order-leastp
 (b* ((bool (twisted-edwards-point-order-leastp point order curve)))
   (booleanp bool))
 :rule-classes :type-prescription)

Theorem: twisted-edwards-point-order-leastp-of-point-fix-point

(defthm twisted-edwards-point-order-leastp-of-point-fix-point
  (equal (twisted-edwards-point-order-leastp (point-fix point)
                                             order curve)
         (twisted-edwards-point-order-leastp point order curve)))

Theorem: twisted-edwards-point-order-leastp-point-equiv-congruence-on-point

(defthm
 twisted-edwards-point-order-leastp-point-equiv-congruence-on-point
 (implies
  (point-equiv point point-equiv)
  (equal
      (twisted-edwards-point-order-leastp point order curve)
      (twisted-edwards-point-order-leastp point-equiv order curve)))
 :rule-classes :congruence)

Theorem: twisted-edwards-point-order-leastp-of-nfix-order

(defthm twisted-edwards-point-order-leastp-of-nfix-order
  (equal (twisted-edwards-point-order-leastp point (nfix order)
                                             curve)
         (twisted-edwards-point-order-leastp point order curve)))

Theorem: twisted-edwards-point-order-leastp-nat-equiv-congruence-on-order

(defthm
   twisted-edwards-point-order-leastp-nat-equiv-congruence-on-order
 (implies
  (nat-equiv order order-equiv)
  (equal
      (twisted-edwards-point-order-leastp point order curve)
      (twisted-edwards-point-order-leastp point order-equiv curve)))
 :rule-classes :congruence)

Theorem: twisted-edwards-point-order-leastp-of-twisted-edwards-curve-fix-curve

(defthm
 twisted-edwards-point-order-leastp-of-twisted-edwards-curve-fix-curve
 (equal (twisted-edwards-point-order-leastp
             point
             order (twisted-edwards-curve-fix curve))
        (twisted-edwards-point-order-leastp point order curve)))

Theorem: twisted-edwards-point-order-leastp-twisted-edwards-curve-equiv-congruence-on-curve

(defthm
 twisted-edwards-point-order-leastp-twisted-edwards-curve-equiv-congruence-on-curve
 (implies
  (twisted-edwards-curve-equiv curve curve-equiv)
  (equal
      (twisted-edwards-point-order-leastp point order curve)
      (twisted-edwards-point-order-leastp point order curve-equiv)))
 :rule-classes :congruence)