def fo_step

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/curve25519/pow.bend:44

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

44# 2^m + (2^m - 1) == 2^(m+1) - 1
45def fo_step(+one: Nat, +h1: {one == 1n : Nat}, +m: Nat) -> {Nat.add(WD.sc(m, one), Fo(one, m)) == Fo(one, 1n+m) : Nat}:
46  +S = WD.sc(m, one)
47  +e1 = Equal.cong(Nat, Nat, t => Nat.sub(t, one), Nat.double(S), Nat.add(S, S), NA.double_self(S))
48  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))))