Consts.cn_lt: 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 171-175 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=171&end_line=175

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/limbs.bend as LV
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/ineq.bend as I
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/bounds.bend as B

def cn_lt(+one: Nat, +h1: {one == 1n : Nat}) -> {Nat.is_lt(FS.cn(one), C.shift(129n, one)) == True{} : Bool}:
  %Equal.sym(Nat, FS.cn(one), Nat.add(FS.digits(one, cn8()), LV.pos(8n, one)), cn_split(one, h1)) : {Nat.is_lt(_, C.shift(129n, one)) == True{} : Bool}
  %Equal.sym(Nat, LV.pos(8n, one), C.shift(128n, one), B.pos_shift(8n, one)) : {Nat.is_lt(Nat.add(FS.digits(one, cn8()), _), C.shift(129n, one)) == True{} : Bool}
  %Equal.sym(Nat, C.shift(129n, one), Nat.add(C.shift(128n, one), C.shift(128n, one)), Equal.sym(Nat, Nat.add(C.shift(128n, one), C.shift(128n, one)), C.shift(129n, one), shift_twice(128n, one))) : {Nat.is_lt(Nat.add(FS.digits(one, cn8()), C.shift(128n, one)), _) == True{} : Bool}
  I.lt_le_add(FS.digits(one, cn8()), C.shift(128n, one), C.shift(128n, one), C.shift(128n, one), I.lt_subst_r(FS.digits(one, cn8()), LV.pos(8n, one), C.shift(128n, one), B.pos_shift(8n, one), digits_lt(one, h1, 8n, cn8(), cn8_limbs(one, h1))), N.le_refl(C.shift(128n, one)))

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=Equal.sym
  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/bounds.bend&name=pos_shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=cn8
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=cn8_limbs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=cn_split
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=digits_lt
  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/crypto/secp256k1/limbs.bend&name=pos
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_refl
  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/crypto/secp256k1/field.bend&name=digits
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift