X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FBridges_LUB.ma;fp=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FBridges_LUB.ma;h=52059ccee753da6d9f1a0929579487f761a332b1;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma new file mode 100644 index 000000000..52059ccee --- /dev/null +++ b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma @@ -0,0 +1,220 @@ +(**************************************************************************) +(* ___ *) +(* ||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 *) +