def pn_sum

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/rconst.bend:65

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
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/proofs/crypto/secp256k1/consts.bend as K

65# p + c_p = n + c_n (= 2^256)
66def pn_sum(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.add(1n+K.pp(one), FS.cp(one)) == Nat.add(1n+K.np(one), FS.cn(one)) : Nat}:
67  Equal.trans(Nat, Nat.add(1n+K.pp(one), FS.cp(one)), C.shift(256n, one), Nat.add(1n+K.np(one), FS.cn(one)), K.hm_p(one, h1), Equal.sym(Nat, Nat.add(1n+K.np(one), FS.cn(one)), C.shift(256n, one), K.hm_n(one, h1)))