Fieldops.negr_le: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend as Fieldops
Lines 126-130 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&start_line=126&end_line=130

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/src/crypto/secp256k1/limbs.bend as L
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend as F
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/consts.bend as K

def negr_le(+one: Nat, +h1: {one == 1n : Nat}, +b: List<&2, Nat>, +hb: {FS.reduced(one, FS.prime(one), b) == True{} : Bool}) -> {Nat.is_le(LV.ev(L.neg_raw(F.c(), b)), C.shift(256n, one)) == True{} : Bool}:
  +m = {1n+K.pp(one) : Nat}
  +nb = LV.ev(L.neg_raw(F.c(), b))
  +mt = I.le_subst_r(m, Nat.add(m, FS.cp(one)), C.shift(256n, one), K.hm_p(one, h1), N.le_add_right(m, FS.cp(one)))
  N.le_trans(nb, m, C.shift(256n, one), I.le_subst_r(nb, Nat.add(nb, LV.ev(b)), m, negr_e(one, h1, b, hb), N.le_add_right(nb, LV.ev(b))), mt)

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=List
  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=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=hm_p
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=pp
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/fieldops.bend&name=negr_e
  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/crypto/secp256k1/limbs.bend&name=ev
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=le_add_right
  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/crypto/secp256k1/field.bend&name=prime
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=reduced
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/field.bend&name=c
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/limbs.bend&name=neg_raw