Proof.scalar_reduce: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/proof.bend as Proof
Lines 42-44 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/proof.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/proof.bend&start_line=42&end_line=44

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend as SE
import bend-collections-laws-crypto@1.0.0.0/src/crypto/ed25519/scalar.bend as ESC
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend as LM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend as S3

def scalar_reduce(+one: Nat, +h1: {one == 1n : Nat}, +bs: List<&2, U32>, +hb: {FS.bytes_ok(64n, bs) == True{} : Bool}) -> SE.Scalar.reduce(one, h1, bs, hb):
  +M = {1n+S3.mmL(one) : Nat}
  Equal.trans(Nat, FS.value(ESC.reduce(bs)), Nat.mod(FS.value(bs), M), Nat.mod(FS.value(bs), SE.ell(one)), S3.reduce_m(one, h1, bs, LM.okb_lea(64n, bs, 255n, ok(64n, bs, hb))), Equal.cong(Nat, Nat, z => Nat.mod(FS.value(bs), z), M, SE.ell(one), ell_m(one, h1)))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.mod
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/limbs.bend&name=okb_lea
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/proof.bend&name=ell_m
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/proof.bend&name=ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend&name=mmL
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend&name=reduce_m
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=bytes_ok
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/curve25519/field.bend&name=value
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend&name=Scalar.reduce
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend&name=ell
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/ed25519/scalar.bend&name=reduce