set "baseuri" "cic:/matita/CoRN-Decl/reals/Max_AbsIR".
+include "CoRN.ma".
+
(* $Id: Max_AbsIR.v,v 1.13 2004/04/23 10:01:04 lcf Exp $ *)
(*#* printing Max %\ensuremath{\max}% *)
(*#* printing Min %\ensuremath{\min}% *)
-(* INCLUDE
-CauchySeq
-*)
+include "reals/CauchySeq.ma".
(* UNEXPORTED
-Section Maximum.
+Section Maximum
*)
(* UNEXPORTED
-Section Max_function.
+Section Max_function
*)
(*#* ** Maximum, Minimum and Absolute Value
%\end{convention}%
*)
-inline cic:/CoRN/reals/Max_AbsIR/x.var.
+alias id "x" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var".
-inline cic:/CoRN/reals/Max_AbsIR/y.var.
+alias id "y" = "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var".
-inline cic:/CoRN/reals/Max_AbsIR/Max_seq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_seq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_seq_char.con".
-inline cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Cauchy_Max_seq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_CauchySeq.con".
-inline cic:/CoRN/reals/Max_AbsIR/MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX.con".
(*#*
Constructively, the elementary properties of the maximum function are:
(So [Max] is [MAX] coupled with some proofs.)
*)
-inline cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/lft_leEq_MAX.con".
-inline cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con.
+inline "cic:/CoRN/reals/Max_AbsIR/rht_leEq_MAX.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con".
(* UNEXPORTED
-End Max_function.
+End Max_function
*)
-inline cic:/CoRN/reals/Max_AbsIR/MAX_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/MAX_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con".
(* UNEXPORTED
-Section properties_of_Max.
+Section properties_of_Max
*)
(*#* *** Maximum *)
-inline cic:/CoRN/reals/Max_AbsIR/Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_wd_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/lft_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/rht_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_Max_imp.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_less.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_less.con".
-inline cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_id.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_id.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_comm.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_comm.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Max_is_rht.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_is_rht_imp_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Max_minus_eps_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/max_one_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/pos_max_one.con.
+inline "cic:/CoRN/reals/Max_AbsIR/pos_max_one.con".
-inline cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con".
(* UNEXPORTED
-End properties_of_Max.
+End properties_of_Max
*)
(* UNEXPORTED
-End Maximum.
+End Maximum
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Minimum.
+Section Minimum
*)
(*#* *** Mininum
[Min(x,y) [=] [--]Max( [--]x,[--]y)].
*)
-inline cic:/CoRN/reals/Max_AbsIR/MIN.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN.con".
-inline cic:/CoRN/reals/Max_AbsIR/MIN_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/MIN_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/MIN_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_wd_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_strext_unfolded.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_lft.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_rht.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_imp.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_Min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_Min.con".
-inline cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con.
+inline "cic:/CoRN/reals/Max_AbsIR/equiv_imp_eq_min.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_id.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_id.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_comm.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_comm.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_imp_Min_is_lft.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_is_lft_imp_leEq.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con".
-inline cic:/CoRN/reals/Max_AbsIR/a.var.
+alias id "a" = "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var".
-inline cic:/CoRN/reals/Max_AbsIR/b.var.
+alias id "b" = "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max'.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min3_leEq_Max3.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ap_imp_Min_less_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con".
(* UNEXPORTED
-End Minimum.
+End Minimum
*)
(*#**********************************)
(* UNEXPORTED
-Section Absolute.
+Section Absolute
*)
(*#**********************************)
(*#* *** Absolute value *)
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/ABSIR_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdl.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_wdr.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIRz_isz.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_nonneg.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_pos.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_cancel_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_resp_ap_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/inv_leEq_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_e.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_imp_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_AbsSmall.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_imp_AbsSmall.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsSmall_transitive.con".
-inline cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con.
+inline "cic:/CoRN/reals/Max_AbsIR/zero_less_AbsIR_plus_one.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_inv.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_minus.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_x.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_inv_x.con".
-inline cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/less_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con.
+inline "cic:/CoRN/reals/Max_AbsIR/leEq_distr_AbsIR.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_approach_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_eq_zero.con".
-inline cic:/CoRN/reals/Max_AbsIR/Abs_Max.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Abs_Max.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_str_bnd.con".
-inline cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con.
+inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con".
(* UNEXPORTED
-End Absolute.
+End Absolute
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Part_Function_Max.
+Section Part_Function_Max
*)
(*#* *** Functional Operators
%\end{convention}%
*)
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var".
(* begin hide *)
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__".
(* end hide *)
-inline cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con.
+inline "cic:/CoRN/reals/Max_AbsIR/part_function_Max_strext.con".
-inline cic:/CoRN/reals/Max_AbsIR/FMax.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMax.con".
(* UNEXPORTED
-End Part_Function_Max.
+End Part_Function_Max
*)
(* UNEXPORTED
-Section Part_Function_Abs.
+Section Part_Function_Abs
*)
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var".
(* begin hide *)
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__".
(* end hide *)
-inline cic:/CoRN/reals/Max_AbsIR/FMin.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMin.con".
-inline cic:/CoRN/reals/Max_AbsIR/FAbs.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs.con".
(* UNEXPORTED
Opaque Max.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FMin_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FMin_char.con".
(* UNEXPORTED
Transparent Max.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_char.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con".
(* UNEXPORTED
-End Part_Function_Abs.
+End Part_Function_Abs
*)
(* UNEXPORTED
Hint Resolve FAbs_char: algebra.
*)
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char'.con".
-inline cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con.
+inline "cic:/CoRN/reals/Max_AbsIR/FAbs_nonneg.con".
(* UNEXPORTED
Hint Resolve FAbs_char': algebra.
*)
(* UNEXPORTED
-Section Inclusion.
+Section Inclusion
*)
-inline cic:/CoRN/reals/Max_AbsIR/F.var.
+alias id "F" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var".
-inline cic:/CoRN/reals/Max_AbsIR/G.var.
+alias id "G" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var".
(* begin hide *)
-inline cic:/CoRN/reals/Max_AbsIR/P.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__".
-inline cic:/CoRN/reals/Max_AbsIR/Q.con.
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__".
(* end hide *)
%\end{convention}%
*)
-inline cic:/CoRN/reals/Max_AbsIR/R.var.
+alias id "R" = "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax'.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMax''.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMax''.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin'.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FMin''.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FMin''.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FAbs.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs.con".
-inline cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con.
+inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con".
(* UNEXPORTED
-End Inclusion.
+End Inclusion
*)
(* UNEXPORTED