--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
+
+include "CoRN.ma".
+
+(* begin hide *)
+
+(* file : least_upper_bound_principle.v *)
+
+(* version : 1.50 - 03/05/2001 *)
+
+(* version : 1.00 - 27/02/2001 *)
+
+(* author : Milad Niqui *)
+
+(* language : coq 7.0beta26feb *)
+
+(* dependency : iso_CReals.v , Expon.v *)
+
+(* description : proof of the Bridges' least upper bound principle *)
+
+include "reals/iso_CReals.ma".
+
+include "algebra/Expon.ma".
+
+(* UNEXPORTED
+Section LUBP
+*)
+
+alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var".
+
+(* SUBSECTION ON GENRAL DEFINITIONS *)
+
+(* UNEXPORTED
+Section lub_definitions
+*)
+
+alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var".
+
+alias id "SS" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var".
+
+inline "cic:/CoRN/reals/Bridges_LUB/member.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/Pmember.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/is_upper_bound.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/l_u_b.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/supremum.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/Psupremum.con".
+
+(* the following definitions are not used in *)
+
+(* this file but later we will need them *)
+
+inline "cic:/CoRN/reals/Bridges_LUB/is_lower_bound.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/g_l_b.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/infimum.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
+
+(* UNEXPORTED
+End lub_definitions
+*)
+
+(* MAIN SECTION *)
+
+(* UNEXPORTED
+Section upper_bound_sequence
+*)
+
+alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var".
+
+alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var".
+
+alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var".
+
+alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/shrink23d.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/shrink13d.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/shrink24d.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/Real_Interval.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.con".
+
+(* NOTATION
+Notation "( p , q )" := (pairT p q).
+*)
+
+inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/Length_dIntrvl.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_l_n.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_n.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/V_increase.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/W_decrease.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_V.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_m_n_W.con".
+
+(* These lemma are *very* similar to those in *)
+
+(* Cauchy_rationals_approach_reals.v *)
+
+inline "cic:/CoRN/reals/Bridges_LUB/a_familiar_simple_inequality.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/CS_seq_U.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_minus_W.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_V_upper.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/U_W_lower.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_V.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.con".
+
+(* Two properties of exponentiation in COrdFields *)
+
+inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_great_One.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.con".
+
+(* A consequence of Archimedean property - *)
+
+(* the every basis of definition of e=lim(1+1/n)^n *)
+
+inline "cic:/CoRN/reals/Bridges_LUB/nexp_resp_Two.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/B_limit_V.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/B_limit_W.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/W_n_is_upper.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con".
+
+inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
+
+(* UNEXPORTED
+End upper_bound_sequence
+*)
+
+(* UNEXPORTED
+End LUBP
+*)
+
+(* end hide *)
+
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