End SIMULATION_SEQUENCES.
(** ** Composing two forward simulations *)
Ltac supertransitivity:=
repeat match goal with
|[|- ?x = ?y] =>
match goal with
| [|- x = x] => reflexivity
| [ H: x = _ |- _ ] => rewrite H in *; clear H
| [ H: _ = x |- _ ] => rewrite H in *; clear H
end
end.

Lemma compose_forward_simulations:
forall L1 L2 L3, forward_simulation L1 L2 -> forward_simulation L2 L3 -> forward_simulation L1 L3.