Scalar3.ell_eq: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend as Scalar3
Lines 56-57 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend&start_line=56&end_line=57

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend as SE
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N

def ell_eq(+one: Nat, +h1: {one == 1n : Nat}) -> {1n+mmL(one) == SE.ell(one) : Nat}:
  N.sub_add(SE.ell(one), 1n, N.le_trans(1n, 2n, SE.ell(one), {==}, ell_ge(one, h1)))

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/scalar3.bend&name=ell_ge
  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/lib/nat.bend&name=le_trans
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=sub_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend&name=ell