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7 (* ||T|| The HELM team. *)
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10 (* \ / This file is distributed under the terms of the *)
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15 (* This file was automatically generated: do not edit *********************)
17 set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
21 (* file : least_upper_bound_principle.v *)
23 (* version : 1.50 - 03/05/2001 *)
25 (* version : 1.00 - 27/02/2001 *)
27 (* author : Milad Niqui *)
29 (* language : coq 7.0beta26feb *)
31 (* dependency : iso_CReals.v , Expon.v *)
33 (* description : proof of the Bridges' least upper bound principle *)
47 inline cic:/CoRN/reals/Bridges_LUB/R1.var.
49 (* SUBSECTION ON GENRAL DEFINITIONS *)
52 Section lub_definitions.
55 inline cic:/CoRN/reals/Bridges_LUB/OF.var.
57 inline cic:/CoRN/reals/Bridges_LUB/SS.var.
59 inline cic:/CoRN/reals/Bridges_LUB/member.con.
61 inline cic:/CoRN/reals/Bridges_LUB/Pmember.con.
63 inline cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con.
65 inline cic:/CoRN/reals/Bridges_LUB/l_u_b.con.
67 inline cic:/CoRN/reals/Bridges_LUB/supremum.con.
69 inline cic:/CoRN/reals/Bridges_LUB/Psupremum.con.
71 (* the following definitions are not used in *)
73 (* this file but later we will need them *)
75 inline cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con.
77 inline cic:/CoRN/reals/Bridges_LUB/g_l_b.con.
79 inline cic:/CoRN/reals/Bridges_LUB/infimum.con.
81 inline cic:/CoRN/reals/Bridges_LUB/Pinfimum.con.
90 Section upper_bound_sequence.
93 inline cic:/CoRN/reals/Bridges_LUB/A.var.
95 inline cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var.
97 inline cic:/CoRN/reals/Bridges_LUB/bounded_above.var.
99 inline cic:/CoRN/reals/Bridges_LUB/located.var.
101 inline cic:/CoRN/reals/Bridges_LUB/s.con.
103 inline cic:/CoRN/reals/Bridges_LUB/Ps.con.
105 inline cic:/CoRN/reals/Bridges_LUB/b0.con.
107 inline cic:/CoRN/reals/Bridges_LUB/Pb0.con.
109 inline cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con.
111 inline cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con.
113 inline cic:/CoRN/reals/Bridges_LUB/dstart_l.con.
115 inline cic:/CoRN/reals/Bridges_LUB/dstart_r.con.
117 inline cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con.
119 inline cic:/CoRN/reals/Bridges_LUB/shrink23d.con.
121 inline cic:/CoRN/reals/Bridges_LUB/shrink13d.con.
123 inline cic:/CoRN/reals/Bridges_LUB/shrink24d.con.
125 inline cic:/CoRN/reals/Bridges_LUB/Real_Interval.con.
127 inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con.
129 inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con.
131 inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con.
133 inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con.
135 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl.con.
137 inline cic:/CoRN/reals/Bridges_LUB/U.con.
139 inline cic:/CoRN/reals/Bridges_LUB/V.con.
141 inline cic:/CoRN/reals/Bridges_LUB/W.con.
143 inline cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con.
145 inline cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con.
147 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con.
149 inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con.
151 inline cic:/CoRN/reals/Bridges_LUB/V_increase.con.
153 inline cic:/CoRN/reals/Bridges_LUB/W_decrease.con.
155 inline cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con.
157 inline cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con.
159 (* These lemma are *very* similar to those in *)
161 (* Cauchy_rationals_approach_reals.v *)
163 inline cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con.
165 inline cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con.
167 inline cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con.
169 inline cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con.
171 inline cic:/CoRN/reals/Bridges_LUB/B.con.
173 inline cic:/CoRN/reals/Bridges_LUB/U_minus_V.con.
175 inline cic:/CoRN/reals/Bridges_LUB/U_minus_W.con.
177 inline cic:/CoRN/reals/Bridges_LUB/U_V_upper.con.
179 inline cic:/CoRN/reals/Bridges_LUB/U_W_lower.con.
181 inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con.
183 inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con.
185 (* Two properties of exponentiation in COrdFields *)
187 inline cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con.
189 inline cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con.
191 (* A consequence of Archimedean property - *)
193 (* the every basis of definition of e=lim(1+1/n)^n *)
195 inline cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con.
197 inline cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con.
199 inline cic:/CoRN/reals/Bridges_LUB/B_limit_V.con.
201 inline cic:/CoRN/reals/Bridges_LUB/B_limit_W.con.
203 inline cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con.
205 inline cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con.
207 inline cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con.
210 End upper_bound_sequence.