set "baseuri" "cic:/matita/CoRN-Decl/ftc/Integral".
-include "CoRN_notation.ma".
+include "CoRN.ma".
(* $Id: Integral.v,v 1.10 2004/04/23 10:00:59 lcf Exp $ *)
(* begin hide *)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
-inline "cic:/CoRN/ftc/Integral/Sumx_wd_weird.con".
+inline "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__".
inline "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* end hide *)
(* UNEXPORTED
-Section Integral.
+Section Integral
*)
(*#* *Integral
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/a.var".
+alias id "a" = "cic:/CoRN/ftc/Integral/Integral/a.var".
-inline "cic:/CoRN/ftc/Integral/b.var".
+alias id "b" = "cic:/CoRN/ftc/Integral/Integral/b.var".
-inline "cic:/CoRN/ftc/Integral/Hab.var".
+alias id "Hab" = "cic:/CoRN/ftc/Integral/Integral/Hab.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/I.con".
+inline "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__".
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Integral/F.var".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/Integral/Integral/contF.var".
-inline "cic:/CoRN/ftc/Integral/contF'.con".
+inline "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__".
(* end hide *)
(* UNEXPORTED
-Section Darboux_Sum.
+Section Darboux_Sum
*)
inline "cic:/CoRN/ftc/Integral/integral_seq.con".
inline "cic:/CoRN/ftc/Integral/integral.con".
(* UNEXPORTED
-End Darboux_Sum.
+End Darboux_Sum
*)
(* UNEXPORTED
-Section Integral_Thm.
+Section Integral_Thm
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/n.var".
+alias id "n" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var".
-inline "cic:/CoRN/ftc/Integral/P.var".
+alias id "P" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var".
-inline "cic:/CoRN/ftc/Integral/e.var".
+alias id "e" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var".
-inline "cic:/CoRN/ftc/Integral/He.var".
+alias id "He" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/d.con".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__".
(* end hide *)
-inline "cic:/CoRN/ftc/Integral/HmeshP.var".
+alias id "HmeshP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var".
-inline "cic:/CoRN/ftc/Integral/fP.var".
+alias id "fP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var".
-inline "cic:/CoRN/ftc/Integral/HfP.var".
+alias id "HfP" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var".
-inline "cic:/CoRN/ftc/Integral/HfP'.var".
+alias id "HfP'" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var".
-inline "cic:/CoRN/ftc/Integral/incF.var".
+alias id "incF" = "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var".
inline "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con".
(* UNEXPORTED
-End Integral_Thm.
+End Integral_Thm
*)
(* UNEXPORTED
-End Integral.
+End Integral
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#*
The usual extensionality and strong extensionality results hold.
*)
-inline "cic:/CoRN/ftc/Integral/a.var".
+alias id "a" = "cic:/CoRN/ftc/Integral/Basic_Properties/a.var".
-inline "cic:/CoRN/ftc/Integral/b.var".
+alias id "b" = "cic:/CoRN/ftc/Integral/Basic_Properties/b.var".
-inline "cic:/CoRN/ftc/Integral/Hab.var".
+alias id "Hab" = "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/I.con".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__".
(* end hide *)
+(* NOTATION
+Notation Integral := (integral _ _ Hab).
+*)
+
(* UNEXPORTED
-Section Well_Definedness.
+Section Well_Definedness
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var".
-inline "cic:/CoRN/ftc/Integral/G.var".
+alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var".
inline "cic:/CoRN/ftc/Integral/integral_strext.con".
inline "cic:/CoRN/ftc/Integral/integral_wd'.con".
(* UNEXPORTED
-End Well_Definedness.
+End Well_Definedness
*)
(* UNEXPORTED
-Section Linearity_and_Monotonicity.
+Section Linearity_and_Monotonicity
*)
(* UNEXPORTED
inline "cic:/CoRN/ftc/Integral/integral_one.con".
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var".
-inline "cic:/CoRN/ftc/Integral/G.var".
+alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var".
inline "cic:/CoRN/ftc/Integral/integral_comm_scal.con".
inline "cic:/CoRN/ftc/Integral/integral_empty.con".
(* UNEXPORTED
-End Linearity_and_Monotonicity.
+End Linearity_and_Monotonicity
*)
(* UNEXPORTED
-Section Linearity_and_Monotonicity'.
+Section Linearity_and_Monotonicity'
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var".
-inline "cic:/CoRN/ftc/Integral/G.var".
+alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var".
(*#*
%\begin{convention}% Let [alpha, beta : IR] and assume that
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/alpha.var".
+alias id "alpha" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var".
-inline "cic:/CoRN/ftc/Integral/beta.var".
+alias id "beta" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/h.con".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__".
(* end hide *)
-inline "cic:/CoRN/ftc/Integral/contH.var".
+alias id "contH" = "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var".
inline "cic:/CoRN/ftc/Integral/linear_integral.con".
*)
(* UNEXPORTED
-End Linearity_and_Monotonicity'.
+End Linearity_and_Monotonicity'
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var".
-inline "cic:/CoRN/ftc/Integral/G.var".
+alias id "G" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+alias id "contF" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+alias id "contG" = "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var".
(*#*
As corollaries we can calculate integrals of group operations applied to functions.
inline "cic:/CoRN/ftc/Integral/integral_leEq_norm.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-Section Integral_Sum.
+Section Integral_Sum
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+alias id "F" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var".
-inline "cic:/CoRN/ftc/Integral/c.var".
+alias id "c" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var".
-inline "cic:/CoRN/ftc/Integral/Hac.var".
+alias id "Hac" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var".
-inline "cic:/CoRN/ftc/Integral/Hcb.var".
+alias id "Hcb" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var".
-inline "cic:/CoRN/ftc/Integral/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var".
-inline "cic:/CoRN/ftc/Integral/Hac'.var".
+alias id "Hac'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var".
-inline "cic:/CoRN/ftc/Integral/Hcb'.var".
+alias id "Hcb'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var".
(* UNEXPORTED
-Section Partition_Join.
+Section Partition_Join
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/n.var".
+alias id "n" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var".
-inline "cic:/CoRN/ftc/Integral/m.var".
+alias id "m" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var".
-inline "cic:/CoRN/ftc/Integral/P.var".
+alias id "P" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var".
-inline "cic:/CoRN/ftc/Integral/Q.var".
+alias id "Q" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var".
(* begin hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/fP.var".
+alias id "fP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var".
-inline "cic:/CoRN/ftc/Integral/HfP.var".
+alias id "HfP" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var".
-inline "cic:/CoRN/ftc/Integral/HfP'.var".
+alias id "HfP'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var".
-inline "cic:/CoRN/ftc/Integral/fQ.var".
+alias id "fQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var".
-inline "cic:/CoRN/ftc/Integral/HfQ.var".
+alias id "HfQ" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var".
-inline "cic:/CoRN/ftc/Integral/HfQ'.var".
+alias id "HfQ'" = "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var".
(* begin hide *)
inline "cic:/CoRN/ftc/Integral/partition_join_mesh.con".
(* UNEXPORTED
-End Partition_Join.
+End Partition_Join
*)
(*#*
inline "cic:/CoRN/ftc/Integral/integral_plus_integral.con".
(* UNEXPORTED
-End Integral_Sum.
+End Integral_Sum
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(*#*