proposition: Lemma L3: injective s.
proof: Proof. assert (mono: forall i j, i < j -> s i t1< s j). { induction 1. - apply L2. - transitivity (s m); auto. apply L2. } intros i j; destruct (lt_eq_lt_dec i j) as [[H0 | Heq] | H0]; [|auto|]; intro e; apply mono in H0; rewrite e in H0; destruct (LT_irrefl H0). Qed.
imports: hydras(Epsilon0 T1) Coq(Ensembles Image Compare_dec)