proposition: Lemma depth_h_absorbs:forall (mu:Matrix) (alpha:Reals) (t: emits_h mu alpha),~(Incl_M mu LL)->~(Incl_M mu RR)->~(Incl_M mu MM)-> forall t', depth_h mu alpha t = S(depth_h (product mu (Streams.hd alpha)) (Streams.tl alpha) t').
proof: Proof. intros mu alpha t t_l t_r t_m t'. transitivity (depth_h mu alpha (emits_h_absorbs _ _ t')). apply depth_h_PI. simpl. case (Incl_M_dec_D mu LL); try contradiction; case (Incl_M_dec_D mu RR); try contradiction; case (Incl_M_dec_D mu MM); try contradiction; intros _; reflexivity. Defined.
imports: digits Refining_M homographic Streams_addenda RIneq QArithSternBrocot(R_addenda) rep