proposition: Lemma reaches_plus_self_loop x : reaches_plus x x -> non_terminating x.
proof: Proof. move=> [k [? Hk]]. elim; first done. move=> k' Hk'. move=> /(steps_k_monotone (k + k')) /(_ ltac:(lia)). by rewrite (steps_plus Hk). Qed.
imports: List ssrfun List PeanoNat Lia Operators_Properties ssreflect ssrbool ssrfun