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[helm.git] / helm / software / matita / contribs / CoRN-Decl / ftc / Integral.ma

diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma
index 920dcdbfc2add4b3780822d9ec4139adf157a078..4a8a416889f63ff203a435def98df31b96ea3eaa 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/ftc/Integral.ma
@@ -16,7 +16,7 @@
 
 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 $ *)
 
@@ -29,21 +29,21 @@ include "ftc/RefLemma.ma".
 (* 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
@@ -59,26 +59,26 @@ continuous functions in [I].
 %\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".
@@ -88,11 +88,11 @@ inline "cic:/CoRN/ftc/Integral/Cauchy_Darboux_Seq.con".
 inline "cic:/CoRN/ftc/Integral/integral.con".
 
 (* UNEXPORTED
-End Darboux_Sum.
+End Darboux_Sum
 *)
 
 (* UNEXPORTED
-Section Integral_Thm.
+Section Integral_Thm
 *)
 
 (*#*
@@ -106,71 +106,75 @@ respecting [P].
 %\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".
 
@@ -181,11 +185,11 @@ inline "cic:/CoRN/ftc/Integral/integral_wd.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
@@ -198,13 +202,13 @@ The integral is a linear and monotonous function; in order to prove these facts
 
 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".
 
@@ -217,20 +221,20 @@ Transparent Even_Partition.
 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
@@ -238,17 +242,17 @@ inline "cic:/CoRN/ftc/Integral/contG.var".
 %\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".
 
@@ -263,20 +267,20 @@ Transparent nring.
 *)
 
 (* 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.
@@ -299,11 +303,11 @@ inline "cic:/CoRN/ftc/Integral/ub_integral.con".
 inline "cic:/CoRN/ftc/Integral/integral_leEq_norm.con".
 
 (* UNEXPORTED
-End Corollaries.
+End Corollaries
 *)
 
 (* UNEXPORTED
-Section Integral_Sum.
+Section Integral_Sum
 *)
 
 (*#*
@@ -315,22 +319,22 @@ $c\in[a,b]$#c∈[a,b]#.
 %\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
 *)
 
 (*#*
@@ -345,13 +349,13 @@ inequality).
 %\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 *)
 
@@ -388,17 +392,17 @@ inline "cic:/CoRN/ftc/Integral/partition_join.con".
 %\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 *)
 
@@ -451,7 +455,7 @@ inline "cic:/CoRN/ftc/Integral/partition_join_Sum_lemma.con".
 inline "cic:/CoRN/ftc/Integral/partition_join_mesh.con".
 
 (* UNEXPORTED
-End Partition_Join.
+End Partition_Join
 *)
 
 (*#*
@@ -465,7 +469,7 @@ Opaque Even_Partition.
 inline "cic:/CoRN/ftc/Integral/integral_plus_integral.con".
 
 (* UNEXPORTED
-End Integral_Sum.
+End Integral_Sum
 *)
 
 (* UNEXPORTED
@@ -473,7 +477,7 @@ Transparent Even_Partition.
 *)
 
 (* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
 *)
 
 (*#*