Notation "s '▷^' n t" := (evaluatesin n s t) (at level 40, n at level 5).
Definition stepplus s t := (exists s', s ≻ s' /\ s' ≻* t).
Notation "s '≻^+' t" := (stepplus s t) (at level 40).

(* Specifications: *)
Lemma unique_step_index s m t n : s ▷^m t -> s ▷^n t -> m = n.
Lemma stepplus_stepn s t : s ≻^+ t <-> exists n, s ≻^(S n) t.
Lemma triangle s n t s' : s ▷^n t -> s ≻^+ s' -> exists k, k < n /\ s' ▷^k t.
Instance step_star_subrelation : subrelation step star.