proposition: Lemma L_omega_square_eqn k : (0 < k)%nat -> L_omega_square k = (exp2 k * (k + 2) - 1)%nat.
proof: Proof. intro Hk; rewrite L_omega_square_eqn1. - rewrite L_omega_mult_eqn; auto. f_equal; abstract lia. Qed.
imports: hydras(E0 Canon Paths) hydras(MoreLists Iterates Exp2) Coq(Lia Compare_dec)