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" as lemma.
28 Section Interval_definition
32 cic:/CoRN/reals/Q_dense/Interval_definition/OF.var
35 inline procedural "cic:/CoRN/reals/Q_dense/Interval.ind".
38 cic:/matita/CoRN-Procedural/reals/Q_dense/pair_crr.con
41 inline procedural "cic:/CoRN/reals/Q_dense/Length.con" as definition.
44 End Interval_definition
47 inline procedural "cic:/CoRN/reals/Q_dense/Rat_Interval.con" as definition.
49 (* we have this in Q_COrdField... *)
51 inline procedural "cic:/CoRN/reals/Q_dense/Qlt_eq_gt_dec'.con" as lemma.
54 Lemma ex_informative_on_Q:(P:Q_as_COrdField->Prop)(Ex [q:Q_as_COrdField](P q))
55 ->{q:Q_as_COrdField | (P q)}.
65 Section COrdField_extra
69 cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var
72 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con" as lemma.
74 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_neg_reflexive.con" as lemma.
76 inline procedural "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con" as lemma.
83 Section Rational_sequence
86 include "tactics/Opaque_algebra.ma".
88 (*#*** WARNING: A file is being loaded *****)
91 cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var
94 inline procedural "cic:/CoRN/reals/Q_dense/start_l.con" as definition.
96 inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence2.con" as lemma.
98 inline procedural "cic:/CoRN/reals/Q_dense/start_r.con" as definition.
100 inline procedural "cic:/CoRN/reals/Q_dense/start_of_sequence_property.con" as lemma.
102 inline procedural "cic:/CoRN/reals/Q_dense/l_less_r.con" as lemma.
104 inline procedural "cic:/CoRN/reals/Q_dense/shrink23.con" as lemma.
106 inline procedural "cic:/CoRN/reals/Q_dense/shrink13.con" as lemma.
108 inline procedural "cic:/CoRN/reals/Q_dense/shrink24.con" as lemma.
110 inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze.con" as definition.
112 inline procedural "cic:/CoRN/reals/Q_dense/cotrans_analyze_strong.con" as lemma.
114 inline procedural "cic:/CoRN/reals/Q_dense/trichotomy.con" as definition.
116 inline procedural "cic:/CoRN/reals/Q_dense/trichotomy_strong1.con" as lemma.
119 Notation "( A , B )" := (pairT A B).
122 inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans.con" as definition.
124 inline procedural "cic:/CoRN/reals/Q_dense/if_cotrans_strong.con" as lemma.
126 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl.con" as definition.
128 inline procedural "cic:/CoRN/reals/Q_dense/G.con" as definition.
134 inline procedural "cic:/CoRN/reals/Q_dense/delta_Intrvl.con" as lemma.
136 inline procedural "cic:/CoRN/reals/Q_dense/Length_Intrvl.con" as lemma.
138 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_l_n.con" as lemma.
140 inline procedural "cic:/CoRN/reals/Q_dense/Intrvl_inside_r_n.con" as lemma.
142 inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_lower.con" as lemma.
144 inline procedural "cic:/CoRN/reals/Q_dense/G_m_n_upper.con" as lemma.
147 Opaque Q_as_COrdField.
150 inline procedural "cic:/CoRN/reals/Q_dense/a_simple_inequality.con" as lemma.
152 inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate2.con" as lemma.
154 inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_G.con" as lemma.
156 inline procedural "cic:/CoRN/reals/Q_dense/G_as_CauchySeq.con" as definition.
158 inline procedural "cic:/CoRN/reals/Q_dense/CS_seq_inj_Q_G.con" as lemma.
160 inline procedural "cic:/CoRN/reals/Q_dense/inj_Q_G_as_CauchySeq.con" as definition.
162 inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_l.con" as lemma.
164 inline procedural "cic:/CoRN/reals/Q_dense/x_in_Intrvl_r.con" as lemma.
166 inline procedural "cic:/CoRN/reals/Q_dense/G_conversion_rate_resp_x.con" as lemma.
168 inline procedural "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con" as lemma.
171 End Rational_sequence