1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
21 include "reals/Q_in_CReals.ma".
23 (*#***** Opaque_algebra.v will be loaded in line 151 ******)
25 inline procedural "cic:/CoRN/reals/Q_dense/or_not_and.con".
28 Section Interval_definition
31 alias id "OF" = "cic:/CoRN/reals/Q_dense/Interval_definition/OF.var".
33 inline procedural "cic:/CoRN/reals/Q_dense/Interval.ind".
36 cic:/matita/CoRN-Procedural/reals/Q_dense/pair_crr.con
39 inline procedural "cic:/CoRN/reals/Q_dense/Length.con".
42 End Interval_definition
45 inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con".
47 (* we have this in Q_COrdField... *)
49 inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con".
52 Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q))
53 ->{q:Q_as_COrdField | (P q)}.
63 Section COrdField_extra
66 alias id "OF" = "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var".
68 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con".
70 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con".
72 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con".
79 Section Rational_sequence
82 include "tactics/Opaque_algebra.ma".
84 (*#*** WARNING: A file is being loaded *****)
86 alias id "R1" = "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var".
88 inline procedural "cic:/CoRN/reals/Q_dense/start_l.con".
90 inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con".
92 inline procedural "cic:/CoRN/reals/Q_dense/start_r.con".
94 inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con".
96 inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con".
98 inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con".
100 inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con".
102 inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con".
104 inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con".
106 inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con".
108 inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con".
110 inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con".
113 Notation "( A , B )" := (pairT A B).
116 inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con".
118 inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con".
120 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con".
122 inline procedural "cic:/CoRN/reals/Q_dense/G.con".
128 inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con".
130 inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con".
132 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con".
134 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con".
136 inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con".
138 inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con".
141 Opaque Q_as_COrdField.
144 inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con".
146 inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con".
148 inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con".
150 inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con".
152 inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con".
154 inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con".
156 inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con".
158 inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con".
160 inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con".
162 inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con".
165 End Rational_sequence