proposition: Lemma phi_inj_r : forall a b c, nf a -> nf b -> nf c -> phi a b = phi a c -> b = c.
proof: Proof. intros a b c Na Nb Nc E; tricho b c H; trivial. - absurd (phi a b t2< phi a c). + rewrite E; apply lt_irr. + apply phi_mono_r;auto. - absurd (phi a c t2< phi a b). + rewrite E; apply lt_irr. + apply phi_mono_r;auto. 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)