proposition: Theorem phi_spec1 : forall alpha beta gamma, nf alpha -> nf beta -> nf gamma -> gamma t2< alpha -> phi gamma (phi alpha beta) = phi alpha beta.
proof: Proof. intros; case (phi_le_ge H H0 ). - intros alpha' (beta', (H'1,(H'2,H'3))); rewrite H'1; cbn. rewrite (compare_rw_lt);auto with T2. apply lt_le_trans with alpha;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)