Pow.fo_step: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend as Pow
Lines 44-48 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&start_line=44&end_line=48

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend as NA

# 2^m + (2^m - 1) == 2^(m+1) - 1
def fo_step(+one: Nat, +h1: {one == 1n : Nat}, +m: Nat) -> {Nat.add(WD.sc(m, one), Fo(one, m)) == Fo(one, 1n+m) : Nat}:
  +S = WD.sc(m, one)
  +e1 = Equal.cong(Nat, Nat, t => Nat.sub(t, one), Nat.double(S), Nat.add(S, S), NA.double_self(S))
  Equal.sym(Nat, Nat.sub(Nat.double(S), one), Nat.add(S, Nat.sub(S, one)), Equal.trans(Nat, Nat.sub(Nat.double(S), one), Nat.sub(Nat.add(S, S), one), Nat.add(S, Nat.sub(S, one)), e1, sub_add_r(S, S, one, one_le_sc(one, h1, m))))

Uses (12):
  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.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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.double
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&name=Fo
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&name=one_le_sc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/curve25519/pow.bend&name=sub_add_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/lemmas/proofs/nat_algebra.bend&name=double_self
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/word.bend&name=sc