def xb_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/scalarpow.bend:173

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/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/semiring.bend as SR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bitsv.bend as BV

173# hv(xb) = c_n + 1
174def xb_v(+one: Nat, +h1: {one == 1n : Nat}) -> {BV.hv(xb(), one, 0n) == Nat.add(FS.cn(one), one) : Nat}:
175  %Equal.sym(List<&2, Nat>, xb(), L.bits(xn()), Equal.sym(List<&2, Nat>, L.bits(xn()), xb(), bits_xb())) : {BV.hv(_, one, 0n) == Nat.add(FS.cn(one), one) : Nat}
176  %Equal.sym(Nat, BV.hv(L.bits(xn()), one, 0n), Nat.add(LV.pos(16n, 0n), FS.digits(one, xn())), BV.bits_v(one, h1, 16n, xn(), 0n, xn_limbs(one, h1))) : {_ == Nat.add(FS.cn(one), one) : Nat}
177  %Equal.sym(Nat, LV.pos(16n, 0n), 0n, LV.pos_zero(16n)) : {Nat.add(_, FS.digits(one, xn())) == Nat.add(FS.cn(one), one) : Nat}
178  %Equal.sym(Nat, FS.digits(one, xn()), Nat.add(FS.cn(one), one), xn_digits(one, h1)) : {Nat.add(0n, _) == Nat.add(FS.cn(one), one) : Nat}
179  %Equal.sym(Nat, Nat.add(0n, Nat.add(FS.cn(one), one)), Nat.add(FS.cn(one), one), SR.zero_add(Nat.add(FS.cn(one), one))) : {_ == Nat.add(FS.cn(one), one) : Nat}
180  {==}