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 *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/algebra/COrdAbs".
24 ** Properties of [AbsSmall]
29 inline cic:/CoRN/algebra/COrdAbs/AbsSmall.con.
32 Implicit Arguments AbsSmall [R].
38 Section AbsSmall_properties.
42 %\begin{convention}% Let [R] be an ordered field.
46 inline cic:/CoRN/algebra/COrdAbs/R.var.
48 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con.
50 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr_unfolded.con.
52 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl.con.
54 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_wdl_unfolded.con.
57 Declare Left Step AbsSmall_wdl_unfolded.
61 Declare Right Step AbsSmall_wdr_unfolded.
68 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_leEq_trans.con.
70 inline cic:/CoRN/algebra/COrdAbs/zero_AbsSmall.con.
72 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_trans.con.
74 inline cic:/CoRN/algebra/COrdAbs/leEq_imp_AbsSmall.con.
76 inline cic:/CoRN/algebra/COrdAbs/inv_resp_AbsSmall.con.
78 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_minus.con.
80 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_plus.con.
82 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div_two.con.
84 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_delta.con.
86 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_delta.con.
88 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_plus_eps_div2.con.
90 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_x_minus_eps_div2.con.
92 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_intermediate.con.
94 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_eps_div2.con.
96 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_nonneg.con.
98 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_mult.con.
100 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_cancel_mult.con.
102 inline cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con.
105 End AbsSmall_properties.
109 Declare Left Step AbsSmall_wdl_unfolded.
113 Declare Right Step AbsSmall_wdr_unfolded.
116 (*#* ** Properties of [AbsBig] *)
118 inline cic:/CoRN/algebra/COrdAbs/absBig.con.
120 inline cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con.
123 Section absBig_wd_properties.
127 %\begin{convention}% Let [R] be an ordered field.
131 inline cic:/CoRN/algebra/COrdAbs/R.var.
133 inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con.
135 inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdl.con.
137 inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdr_unfolded.con.
139 inline cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con.
142 End absBig_wd_properties.
146 Declare Left Step AbsBig_wdl_unfolded.
150 Declare Right Step AbsBig_wdr_unfolded.