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Secp256k1-point

Secp256k1-point->x

Get the x field from a secp256k1-point.

Signature
(secp256k1-point->x p) → x
Arguments: p — Guard (secp256k1-pointp p).
Returns: x — Type (secp256k1-fieldp x).

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

Definitions and Theorems

Function: secp256k1-point->x$inline

(defun secp256k1-point->x$inline (p)
  (declare (xargs :guard (secp256k1-pointp p)))
  (declare (xargs :guard t))
  (let ((acl2::__function__ 'secp256k1-point->x))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((p (and t p)))
           (secp256k1-field-fix (std::da-nth 0 p)))
         :exec (std::da-nth 0 p))))

Theorem: secp256k1-fieldp-of-secp256k1-point->x

(defthm secp256k1-fieldp-of-secp256k1-point->x
  (b* ((x (secp256k1-point->x$inline p)))
    (secp256k1-fieldp x))
  :rule-classes :rewrite)

Theorem: secp256k1-point->x$inline-of-secp256k1-point-fix-p

(defthm secp256k1-point->x$inline-of-secp256k1-point-fix-p
  (equal (secp256k1-point->x$inline (secp256k1-point-fix p))
         (secp256k1-point->x$inline p)))

Theorem: secp256k1-point->x$inline-secp256k1-point-equiv-congruence-on-p

(defthm
    secp256k1-point->x$inline-secp256k1-point-equiv-congruence-on-p
  (implies (secp256k1-point-equiv p p-equiv)
           (equal (secp256k1-point->x$inline p)
                  (secp256k1-point->x$inline p-equiv)))
  :rule-classes :congruence)