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).

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.