Consts.cp_hb: 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 92-98 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=92&end_line=98

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

def cp_hb(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_le(Nat.add(Nat.mul(1n+FS.cp(one), FS.cp(one)), FS.cp(one)), C.shift(256n, one)) == True{} : Bool}:
  +c = FS.cp(one)
  +s1 = I.le_mul2(1n+c, c, C.shift(34n, one), C.shift(33n, one), cp_succ_le(one, h1), cp_le(one, h1))
  +s2 = I.le_subst_r(Nat.mul(1n+c, c), Nat.mul(C.shift(34n, one), C.shift(33n, one)), C.shift(67n, one), shift_mul2(one, h1, 34n, 33n), s1)
  +s3 = I.le_add2(Nat.mul(1n+c, c), c, C.shift(67n, one), C.shift(67n, one), s2, N.le_trans(c, C.shift(33n, one), C.shift(67n, one), cp_le(one, h1), shift_le_k(33n, 67n, one, 34n, {==})))
  +s4 = I.le_subst_r(Nat.add(Nat.mul(1n+c, c), c), Nat.add(C.shift(67n, one), C.shift(67n, one)), C.shift(68n, one), shift_twice(67n, one), s3)
  N.le_trans(Nat.add(Nat.mul(1n+c, c), c), C.shift(68n, one), C.shift(256n, one), s4, shift_le_k(68n, 256n, one, 188n, {==}))

Uses (16):
  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=cp_le
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=cp_succ_le
  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=shift_mul2
  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=le_add2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend&name=le_mul2
  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/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=cp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift