intros p n s s1 s2 s' i i1 i2 i' H1 H2 H3.
generalize (step_deterministic _ _ _ _ _ _ _ H1 H2).
intuition; subst; auto.
Qed.

Lemma step_triangle : forall p n1 n2 s s1 s2 i i1 i2,
n1 <= n2 ->
stepN p n1 s i s1 i1 ->
stepN p n2 s i s2 i2 ->
stepN p (n2 - n1) s1 i1 s2 i2.