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Group-arithmetic-operations

Op-group-neg

Leo group negation operation.

Signature
(op-group-neg arg curve) → result
Arguments: arg — Guard (valuep arg).; curve — Guard (curvep curve).
Returns: result — Type (value-resultp result).

Definitions and Theorems

Function: op-group-neg

(defun op-group-neg (arg curve)
  (declare (xargs :guard (and (valuep arg) (curvep curve))))
  (declare (xargs :guard (value-case arg :group)))
  (let ((__function__ 'op-group-neg))
    (declare (ignorable __function__))
    (b* ((x (value-group->get arg))
         ((unless (curve-subgroupp x curve))
          (reserrf (list :input-not-in-subgroup x)))
         ((mv okp -x)
          (curve-subgroup-neg x curve))
         ((unless okp)
          (reserrf (list :output-not-in-subgroup -x))))
      (value-group -x))))

Theorem: value-resultp-of-op-group-neg

(defthm value-resultp-of-op-group-neg
  (b* ((result (op-group-neg arg curve)))
    (value-resultp result))
  :rule-classes :rewrite)

Theorem: op-group-neg-of-value-fix-arg

(defthm op-group-neg-of-value-fix-arg
  (equal (op-group-neg (value-fix arg) curve)
         (op-group-neg arg curve)))

Theorem: op-group-neg-value-equiv-congruence-on-arg

(defthm op-group-neg-value-equiv-congruence-on-arg
  (implies (value-equiv arg arg-equiv)
           (equal (op-group-neg arg curve)
                  (op-group-neg arg-equiv curve)))
  :rule-classes :congruence)

Theorem: op-group-neg-of-curve-fix-curve

(defthm op-group-neg-of-curve-fix-curve
  (equal (op-group-neg arg (curve-fix curve))
         (op-group-neg arg curve)))

Theorem: op-group-neg-curve-equiv-congruence-on-curve

(defthm op-group-neg-curve-equiv-congruence-on-curve
  (implies (curve-equiv curve curve-equiv)
           (equal (op-group-neg arg curve)
                  (op-group-neg arg curve-equiv)))
  :rule-classes :congruence)