set "baseuri" "cic:/matita/CoRN-Decl/algebra/CSums".
+include "CoRN.ma".
+
(* $Id: CSums.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
(*#* printing Sum0 %\ensuremath{\sum_0}% #∑<sub>0</sub># *)
(*#* printing Sumx %\ensuremath{\sum'}% #∑'&*)
-(* INCLUDE
-CAbGroups
-*)
-
-(* INCLUDE
-Peano_dec
-*)
+include "algebra/CAbGroups.ma".
(*#* * Sums
*)
(* UNEXPORTED
-Section Sums.
+Section Sums
*)
-inline cic:/CoRN/algebra/CSums/G.var.
+alias id "G" = "cic:/CoRN/algebra/CSums/Sums/G.var".
(* Sum1 and Sum use subtraction *)
-inline cic:/CoRN/algebra/CSums/Sumlist.con.
+inline "cic:/CoRN/algebra/CSums/Sumlist.con".
-inline cic:/CoRN/algebra/CSums/Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx.con".
(*#*
It is sometimes useful to view a function defined on $\{0,\ldots,i-1\}$
[Zero] when the input is greater than or equal to [i].
*)
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun.con".
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch1.con".
-inline cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con.
+inline "cic:/CoRN/algebra/CSums/part_tot_nat_fun_ch2.con".
(*#* [Sum0] defines the sum for [i=0..(n-1)] *)
-inline cic:/CoRN/algebra/CSums/Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sum0.con".
(*#* [Sum1] defines the sum for [i=m..(n-1)] *)
-inline cic:/CoRN/algebra/CSums/Sum1.con.
+inline "cic:/CoRN/algebra/CSums/Sum1.con".
-inline cic:/CoRN/algebra/CSums/Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum.con".
(* Sum i=m..n *)
(*#* [Sum2] is similar to [Sum1], but does not require the summand to be
defined outside where it is being added. *)
-inline cic:/CoRN/algebra/CSums/Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_one.con.
+inline "cic:/CoRN/algebra/CSums/Sum_one.con".
(* UNEXPORTED
Hint Resolve Sum_one: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_empty.con.
+inline "cic:/CoRN/algebra/CSums/Sum_empty.con".
(* UNEXPORTED
Hint Resolve Sum_empty: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_Sum.con".
(* UNEXPORTED
Hint Resolve Sum_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_first.con.
+inline "cic:/CoRN/algebra/CSums/Sum_first.con".
-inline cic:/CoRN/algebra/CSums/Sum_last.con.
+inline "cic:/CoRN/algebra/CSums/Sum_last.con".
(* UNEXPORTED
Hint Resolve Sum_last: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_last'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_last'.con".
(*#*
We add some extensionality results which will be quite useful
when working with integration.
*)
-inline cic:/CoRN/algebra/CSums/Sum0_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_strext.con".
-inline cic:/CoRN/algebra/CSums/Sum_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sum_strext.con".
-inline cic:/CoRN/algebra/CSums/Sumx_strext.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_strext.con".
-inline cic:/CoRN/algebra/CSums/Sum0_strext'.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_strext'.con".
-inline cic:/CoRN/algebra/CSums/Sum_strext'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_strext'.con".
-inline cic:/CoRN/algebra/CSums/Sum0_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum_wd.con".
-inline cic:/CoRN/algebra/CSums/Sumx_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum_wd'.con.
+inline "cic:/CoRN/algebra/CSums/Sum_wd'.con".
-inline cic:/CoRN/algebra/CSums/Sum2_wd.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_wd.con".
-inline cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_plus_Sum0.con".
(* UNEXPORTED
Hint Resolve Sum0_plus_Sum0: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_plus_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_plus_Sum.con".
-inline cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_plus_Sumx.con".
-inline cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_plus_Sum2.con".
-inline cic:/CoRN/algebra/CSums/inv_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum0.con".
(* UNEXPORTED
Hint Resolve inv_Sum0: algebra.
*)
-inline cic:/CoRN/algebra/CSums/inv_Sum.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum.con".
(* UNEXPORTED
Hint Resolve inv_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/inv_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sumx.con".
-inline cic:/CoRN/algebra/CSums/inv_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/inv_Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_minus_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sum_minus_Sum.con".
(* UNEXPORTED
Hint Resolve Sum_minus_Sum: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_minus_Sumx.con".
-inline cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con.
+inline "cic:/CoRN/algebra/CSums/Sum2_minus_Sum2.con".
-inline cic:/CoRN/algebra/CSums/Sum_apzero.con.
+inline "cic:/CoRN/algebra/CSums/Sum_apzero.con".
-inline cic:/CoRN/algebra/CSums/Sum_zero.con.
+inline "cic:/CoRN/algebra/CSums/Sum_zero.con".
-inline cic:/CoRN/algebra/CSums/Sum_term.con.
+inline "cic:/CoRN/algebra/CSums/Sum_term.con".
-inline cic:/CoRN/algebra/CSums/Sum0_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum0_shift.con".
(* UNEXPORTED
Hint Resolve Sum0_shift: algebra.
*)
-inline cic:/CoRN/algebra/CSums/Sum_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum_shift.con".
-inline cic:/CoRN/algebra/CSums/Sum_big_shift.con.
+inline "cic:/CoRN/algebra/CSums/Sum_big_shift.con".
-inline cic:/CoRN/algebra/CSums/Sumx_Sum0.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_Sum0.con".
(* UNEXPORTED
-End Sums.
+End Sums
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Sums.
+Section More_Sums
*)
-inline cic:/CoRN/algebra/CSums/G.var.
+alias id "G" = "cic:/CoRN/algebra/CSums/More_Sums/G.var".
-inline cic:/CoRN/algebra/CSums/Mengolli_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Mengolli_Sum.con".
-inline cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con.
+inline "cic:/CoRN/algebra/CSums/Mengolli_Sum_gen.con".
-inline cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con.
+inline "cic:/CoRN/algebra/CSums/str_Mengolli_Sum_gen.con".
-inline cic:/CoRN/algebra/CSums/Sumx_to_Sum.con.
+inline "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con".
(* UNEXPORTED
-End More_Sums.
+End More_Sums
*)
(* UNEXPORTED