X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fcontribs%2FCoRN-Decl%2Freals%2FBridges_LUB.ma;h=9ebc968429e108a014f0e226984b992de2917222;hb=62596f4e0a109e43c9df5da20571827c8b905ce4;hp=1ec3771ae38ba36a27ccef0f1f4f33f723ee9b8c;hpb=0e0d5c57eb154bf20d101f09e560401434156c1d;p=helm.git diff --git a/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma index 1ec3771ae..9ebc96842 100644 --- a/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma +++ b/matita/contribs/CoRN-Decl/reals/Bridges_LUB.ma @@ -16,6 +16,8 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB". +include "CoRN.ma". + (* begin hide *) (* file : least_upper_bound_principle.v *) @@ -32,186 +34,186 @@ set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB". (* description : proof of the Bridges' least upper bound principle *) -(* INCLUDE -iso_CReals -*) +include "reals/iso_CReals.ma". -(* INCLUDE -Expon -*) +include "algebra/Expon.ma". (* UNEXPORTED -Section LUBP. +Section LUBP *) -inline cic:/CoRN/reals/Bridges_LUB/R1.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var" "LUBP__". (* SUBSECTION ON GENRAL DEFINITIONS *) (* UNEXPORTED -Section lub_definitions. +Section lub_definitions *) -inline cic:/CoRN/reals/Bridges_LUB/OF.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var" "LUBP__lub_definitions__". -inline cic:/CoRN/reals/Bridges_LUB/SS.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var" "LUBP__lub_definitions__". -inline cic:/CoRN/reals/Bridges_LUB/member.con. +inline "cic:/CoRN/reals/Bridges_LUB/member.con". -inline cic:/CoRN/reals/Bridges_LUB/Pmember.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/is_upper_bound.con". -inline cic:/CoRN/reals/Bridges_LUB/l_u_b.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/supremum.con". -inline cic:/CoRN/reals/Bridges_LUB/Psupremum.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/is_lower_bound.con". -inline cic:/CoRN/reals/Bridges_LUB/g_l_b.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/infimum.con". -inline cic:/CoRN/reals/Bridges_LUB/Pinfimum.con. +inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con". (* UNEXPORTED -End lub_definitions. +End lub_definitions *) (* MAIN SECTION *) (* UNEXPORTED -Section upper_bound_sequence. +Section upper_bound_sequence *) -inline cic:/CoRN/reals/Bridges_LUB/A.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/bounded_above.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/located.var. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/s.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/Ps.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/b0.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/Pb0.con. +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/b0_is_upper_bound.con". -inline cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con. +inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con". -inline cic:/CoRN/reals/Bridges_LUB/dstart_l.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/dstart_r.con. +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/dl_less_dr.con". -inline cic:/CoRN/reals/Bridges_LUB/shrink23d.con. +inline "cic:/CoRN/reals/Bridges_LUB/shrink23d.con". -inline cic:/CoRN/reals/Bridges_LUB/shrink13d.con. +inline "cic:/CoRN/reals/Bridges_LUB/shrink13d.con". -inline cic:/CoRN/reals/Bridges_LUB/shrink24d.con. +inline "cic:/CoRN/reals/Bridges_LUB/shrink24d.con". -inline cic:/CoRN/reals/Bridges_LUB/Real_Interval.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.con". -inline cic:/CoRN/reals/Bridges_LUB/dcotrans_analyze_strong.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.con". -inline cic:/CoRN/reals/Bridges_LUB/dif_cotrans_strong.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/dIntrvl.con". -inline cic:/CoRN/reals/Bridges_LUB/U.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/V.con. +inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__". -inline cic:/CoRN/reals/Bridges_LUB/W.con. +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/delta_dIntrvl.con". -inline cic:/CoRN/reals/Bridges_LUB/Length_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_l_n.con". -inline cic:/CoRN/reals/Bridges_LUB/dIntrvl_inside_r_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/V_increase.con". -inline cic:/CoRN/reals/Bridges_LUB/W_decrease.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_V.con". -inline cic:/CoRN/reals/Bridges_LUB/U_m_n_W.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/a_familiar_simple_inequality.con". -inline cic:/CoRN/reals/Bridges_LUB/U_conversion_rate2.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/CS_seq_U.con". -inline cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con. +inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con". -inline cic:/CoRN/reals/Bridges_LUB/B.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_V.con". -inline cic:/CoRN/reals/Bridges_LUB/U_minus_W.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_V_upper.con". -inline cic:/CoRN/reals/Bridges_LUB/U_W_lower.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_V.con". -inline cic:/CoRN/reals/Bridges_LUB/AbsSmall_U_W.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/nexp_resp_great_One.con". -inline cic:/CoRN/reals/Bridges_LUB/very_weak_binomial.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/nexp_resp_Two.con". -inline cic:/CoRN/reals/Bridges_LUB/twisted_archimedean.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_V.con". -inline cic:/CoRN/reals/Bridges_LUB/B_limit_W.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/W_n_is_upper.con". -inline cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con. +inline "cic:/CoRN/reals/Bridges_LUB/A_bounds_V_n.con". -inline cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con. +inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con". (* UNEXPORTED -End upper_bound_sequence. +End upper_bound_sequence *) (* UNEXPORTED -End LUBP. +End LUBP *) (* end hide *)