proposition: Lemma as_Moebius_Q_R: forall x, Zero<(-x)+3->as_Moebius_Q RR x= (x+1)/((-x)+3).
proof: Proof. intros x H_x; assert (H_x':(-x) * 2 + 3 * 2 <> Zero); [stepl (2*((-x)+3)); auto; ring|]; unfold as_Moebius_Q, map_digits, fst, snd, Qdiv at 2; replace ((-1)%Z/2*x) with (-x/2); [|rewrite Z_to_Q_min_one; field; auto]; rewrite <- Qmult_assoc; rewrite Qmult_one_left; rewrite Qmult_sym; fold (Qdiv x 2); rewrite Qplus_Qdiv; auto; rewrite Qplus_Qdiv; auto; rewrite Qdiv_Qdiv_simplify; auto; field; auto. Qed.
imports: Streams Streams_addenda Raxioms