proposition: Lemma T1_to_T2_inj : forall alpha beta : T1, T1_to_T2 alpha = T1_to_T2 beta -> alpha = beta.
proof: Proof. induction alpha; destruct beta;simpl;auto with T2. - discriminate 1. - discriminate 1. - injection 1;auto with T2. rewrite (IHalpha1 beta1), (IHalpha2 beta2). + destruct 2;auto with T2. + injection H;auto with T2. + injection H;auto 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)