def pinf_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/pmul.bend:49

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 SL

49def pinf_v(+one: Nat, +h1: {one == 1n : Nat}) -> {PT.pv(one, P.infinity()) == CV.infinity() : CV.SPoint}:
50  %Equal.sym(Nat, FS.value(one, F.zero()), 0n, PT.zero_v(one, h1)) : {CV.SPoint{_, FS.value(one, F.small(1n)), FS.value(one, F.zero())} == CV.SPoint{0n, 1n, 0n} : CV.SPoint}
51  %Equal.sym(Nat, FS.value(one, F.zero()), 0n, PT.zero_v(one, h1)) : {CV.SPoint{0n, FS.value(one, F.small(1n)), _} == CV.SPoint{0n, 1n, 0n} : CV.SPoint}
52  %Equal.sym(Nat, FS.value(one, F.small(1n)), 1n, FO.small_val(one, h1, 1n, SL.one_lt(one, h1))) : {CV.SPoint{0n, _, 0n} == CV.SPoint{0n, 1n, 0n} : CV.SPoint}
53  {==}