Consts.cn_cc: 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 177-182 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=177&end_line=182

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/crypto/secp256k1/ineq.bend as I

# the fold bounds for n: 2 c < 2^256, (1 + c) c <= 4 2^256, 5 c + c <= 2^256
def cn_cc(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_lt(Nat.add(FS.cn(one), FS.cn(one)), C.shift(256n, one)) == True{} : Bool}:
  +c = FS.cn(one)
  +s1 = I.lt_le_add(c, c, C.shift(129n, one), C.shift(129n, one), cn_lt(one, h1), N.lt_le(c, C.shift(129n, one), cn_lt(one, h1)))
  +s2 = I.lt_subst_r(Nat.add(c, c), Nat.add(C.shift(129n, one), C.shift(129n, one)), C.shift(130n, one), shift_twice(129n, one), s1)
  N.lt_trans(Nat.add(c, c), C.shift(130n, one), C.shift(256n, one), s2, shift_lt_k(one, h1, 130n, 256n, 125n, {==}))

Uses (13):
  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_lt
  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=shift_lt_k
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=shift_twice
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=lt_le_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=lt_subst_r
  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/proofs/lib/nat.bend&name=lt_trans
  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