set "baseuri" "cic:/matita/CoRN-Decl/reals/Bridges_LUB".
+include "CoRN.ma".
+
(* begin hide *)
(* file : least_upper_bound_principle.v *)
(* 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.
+alias id "R1" = "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var".
(* SUBSECTION ON GENRAL DEFINITIONS *)
(* UNEXPORTED
-Section lub_definitions.
+Section lub_definitions
*)
-inline cic:/CoRN/reals/Bridges_LUB/OF.var.
+alias id "OF" = "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var".
-inline cic:/CoRN/reals/Bridges_LUB/SS.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/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.
+alias id "A" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var".
-inline cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var.
+alias id "is_inhabitted" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var".
-inline cic:/CoRN/reals/Bridges_LUB/bounded_above.var.
+alias id "bounded_above" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var".
-inline cic:/CoRN/reals/Bridges_LUB/located.var.
+alias id "located" = "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var".
-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 *)