def g_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/paff.bend:80

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/point.bend as P
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as FO
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as PM

80def g_v(+one: Nat, +h1: {one == 1n : Nat}) -> {PT.pv(one, P.g()) == CV.g(one) : CV.SPoint}:
81  %Equal.sym(Nat, FS.value(one, F.small(1n)), 1n, FO.small_val(one, h1, 1n, PM.one_lt(one, h1))) : {CV.SPoint{FS.value(one, P.gx()), FS.value(one, P.gy()), _} == CV.g(one) : CV.SPoint}
82  Equal.cong(Nat, CV.SPoint, z => CV.SPoint{FS.value(one, P.gx()), FS.value(one, P.gy()), z}, 1n, one, Equal.sym(Nat, one, 1n, h1))