Scalarops.red_v: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend as Scalarops
Lines 68-72 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&start_line=68&end_line=72

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/scalar.bend as S
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/consts.bend as K

def red_v(+one: Nat, +h1: {one == 1n : Nat}, +xs: List<&2, Nat>, +hx: {Nat.is_lt(LV.ev(xs), Nat.mul(C.shift(256n, one), C.shift(256n, one))) == True{} : Bool}) -> {FS.value(one, S.reduce_u(xs)) == Nat.mod(LV.ev(xs), FS.order(one)) : Nat}:
  %Equal.sym(Nat, FS.value(one, S.reduce_u(xs)), LV.ev(S.reduce_u(xs)), LV.ev_value(one, h1, S.reduce_u(xs))) : {_ == Nat.mod(LV.ev(xs), FS.order(one)) : Nat}
  %Equal.sym(Nat, LV.ev(S.reduce_u(xs)), Nat.mod(LV.ev(xs), 1n+K.np(one)), red_e(one, h1, xs, hx)) : {_ == Nat.mod(LV.ev(xs), FS.order(one)) : Nat}
  %Equal.sym(Nat, 1n+K.np(one), FS.order(one), Equal.sym(Nat, FS.order(one), 1n+K.np(one), K.order_eq(one, h1))) : {Nat.mod(LV.ev(xs), _) == Nat.mod(LV.ev(xs), FS.order(one)) : Nat}
  {==}

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=Equal.sym
  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.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  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=np
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/consts.bend&name=order_eq
  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/crypto/secp256k1/limbs.bend&name=ev_value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/scalarops.bend&name=red_e
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=order
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend&name=value
  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/scalar.bend&name=reduce_u