Consts.cn_hb2: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend as Consts
Lines 211-217 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&start_line=211&end_line=217

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/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I

def cn_hb2(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.add(Nat.mul(5n, FS.cn(one)), FS.cn(one)), C.shift(256n, one)) == True{} : Bool}:
  +c = FS.cn(one)
  +l = N.lt_le(c, C.shift(129n, one), cn_lt(one, h1))
  +s1 = I.le_add2(Nat.mul(5n, c), c, Nat.mul(5n, C.shift(129n, one)), C.shift(129n, one), I.le_mul_r(5n, c, C.shift(129n, one), l), l)
  +s2 = I.le_subst_r(Nat.add(Nat.mul(5n, c), c), Nat.add(Nat.mul(5n, C.shift(129n, one)), C.shift(129n, one)), Nat.mul(6n, C.shift(129n, one)), six(C.shift(129n, one)), s1)
  +s3 = N.le_trans(Nat.mul(6n, C.shift(129n, one)), Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), AR.mul_le(6n, 8n, C.shift(129n, one), {==}), I.le_subst_r(Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), C.shift(132n, one), {==}, N.eq_le(Nat.mul(8n, C.shift(129n, one)), C.shift(132n, one), eight(C.shift(129n, one)))))
  N.le_trans(Nat.add(Nat.mul(5n, c), c), Nat.mul(6n, C.shift(129n, one)), C.shift(256n, one), s2, N.le_trans(Nat.mul(6n, C.shift(129n, one)), C.shift(132n, one), C.shift(256n, one), s3, shift_le_k(132n, 256n, one, 124n, {==})))

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=cn_lt
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=eight
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=shift_le_k
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=six
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=le_add2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=le_mul_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=le_subst_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/arith.bend&name=mul_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=eq_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=cn
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift