proposition: Theorem subterm_lt alpha beta: subterm alpha beta -> nf beta -> alpha t2< beta.
proof: Proof. induction 1;auto with T2. - intro;apply lt_tail;auto with T2. - intro; apply lt_trans with t1;auto with T2. eapply IHsubterm1; eapply nf_subterm;eauto with T2. Qed.
imports: Coq(Arith List Lia Compare_dec Relations Wellfounded RelationClasses) hydras(Epsilon0) hydras(More_Arith Restriction) hydras(ON_Generic) hydras(rpo.term rpo.rpo) hydras(T2) hydras(Compat815)