freescale porting, work in progress

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

diff --git a/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma b/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma
index 6042eee7a3dfa42a7f6a00598bd9c4fc07b8919e..481eb2b3b4663b38f20eaa363ad7f563a3bb6c04 100644 (file)
--- a/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma
+++ b/helm/software/matita/contribs/CoRN-Decl/ftc/FTC.ma
@@ -16,24 +16,22 @@
 
 set "baseuri" "cic:/matita/CoRN-Decl/ftc/FTC".
 
+include "CoRN.ma".
+
 (* $Id: FTC.v,v 1.5 2004/04/23 10:00:58 lcf Exp $ *)
 
 (*#* printing [-S-] %\ensuremath{\int}% #∫# *)
 
-(* INCLUDE
-MoreIntegrals
-*)
+include "ftc/MoreIntegrals.ma".
 
-(* INCLUDE
-CalculusTheorems
-*)
+include "ftc/CalculusTheorems.ma".
 
 (* UNEXPORTED
 Opaque Min.
 *)
 
 (* UNEXPORTED
-Section Indefinite_Integral.
+Section Indefinite_Integral
 *)
 
 (*#* *The Fundamental Theorem of Calculus
@@ -53,32 +51,36 @@ and [a] be a point in [I].
 %\end{convention}%
 *)
 
-inline cic:/CoRN/ftc/FTC/I.var.
+alias id "I" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var".
 
-inline cic:/CoRN/ftc/FTC/F.var.
+alias id "F" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var".
 
-inline cic:/CoRN/ftc/FTC/contF.var.
+alias id "contF" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var".
 
-inline cic:/CoRN/ftc/FTC/a.var.
+alias id "a" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var".
 
-inline cic:/CoRN/ftc/FTC/Ha.var.
+alias id "Ha" = "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var".
 
-inline cic:/CoRN/ftc/FTC/prim_lemma.con.
+inline "cic:/CoRN/ftc/FTC/prim_lemma.con".
 
-inline cic:/CoRN/ftc/FTC/Fprim_strext.con.
+inline "cic:/CoRN/ftc/FTC/Fprim_strext.con".
 
-inline cic:/CoRN/ftc/FTC/Fprim.con.
+inline "cic:/CoRN/ftc/FTC/Fprim.con".
 
 (* UNEXPORTED
-End Indefinite_Integral.
+End Indefinite_Integral
 *)
 
 (* UNEXPORTED
 Implicit Arguments Fprim [I F].
 *)
 
+(* NOTATION
+Notation "[-S-] F" := (Fprim F) (at level 20).
+*)
+
 (* UNEXPORTED
-Section FTC.
+Section FTC
 *)
 
 (*#* **The FTC
@@ -92,41 +94,41 @@ indefinite integral of [F] from [x0].
 %\end{convention}%
 *)
 
-inline cic:/CoRN/ftc/FTC/J.var.
+alias id "J" = "cic:/CoRN/ftc/FTC/FTC/J.var".
 
-inline cic:/CoRN/ftc/FTC/F.var.
+alias id "F" = "cic:/CoRN/ftc/FTC/FTC/F.var".
 
-inline cic:/CoRN/ftc/FTC/contF.var.
+alias id "contF" = "cic:/CoRN/ftc/FTC/FTC/contF.var".
 
-inline cic:/CoRN/ftc/FTC/x0.var.
+alias id "x0" = "cic:/CoRN/ftc/FTC/FTC/x0.var".
 
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+alias id "Hx0" = "cic:/CoRN/ftc/FTC/FTC/Hx0.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__".
 
 (* end hide *)
 
-inline cic:/CoRN/ftc/FTC/Continuous_prim.con.
+inline "cic:/CoRN/ftc/FTC/Continuous_prim.con".
 
 (*#*
 The derivative of [G] is simply [F].
 *)
 
-inline cic:/CoRN/ftc/FTC/pJ.var.
+alias id "pJ" = "cic:/CoRN/ftc/FTC/FTC/pJ.var".
 
-inline cic:/CoRN/ftc/FTC/FTC1.con.
+inline "cic:/CoRN/ftc/FTC/FTC1.con".
 
 (*#*
 Any other function [G0] with derivative [F] must differ from [G] by a constant.
 *)
 
-inline cic:/CoRN/ftc/FTC/G0.var.
+alias id "G0" = "cic:/CoRN/ftc/FTC/FTC/G0.var".
 
-inline cic:/CoRN/ftc/FTC/derG0.var.
+alias id "derG0" = "cic:/CoRN/ftc/FTC/FTC/derG0.var".
 
-inline cic:/CoRN/ftc/FTC/FTC2.con.
+inline "cic:/CoRN/ftc/FTC/FTC2.con".
 
 (*#*
 The following is another statement of the Fundamental Theorem of Calculus, also known as Barrow's rule.
@@ -134,7 +136,7 @@ The following is another statement of the Fundamental Theorem of Calculus, also
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FTC/G0_inc.con.
+inline "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__".
 
 (* end hide *)
 
@@ -142,12 +144,12 @@ inline cic:/CoRN/ftc/FTC/G0_inc.con.
 Opaque G.
 *)
 
-inline cic:/CoRN/ftc/FTC/Barrow.con.
+inline "cic:/CoRN/ftc/FTC/Barrow.con".
 
 (* end hide *)
 
 (* UNEXPORTED
-End FTC.
+End FTC
 *)
 
 (* UNEXPORTED
@@ -159,7 +161,7 @@ Hint Resolve FTC1: derivate.
 *)
 
 (* UNEXPORTED
-Section Limit_of_Integral_Seq.
+Section Limit_of_Integral_Seq
 *)
 
 (*#* **Corollaries
@@ -178,18 +180,18 @@ then the sequence of their primitives also converges, and the limit
 commutes with the indefinite integral.
 *)
 
-inline cic:/CoRN/ftc/FTC/J.var.
+alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var".
 
-inline cic:/CoRN/ftc/FTC/f.var.
+alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var".
 
-inline cic:/CoRN/ftc/FTC/F.var.
+alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var".
 
-inline cic:/CoRN/ftc/FTC/contf.var.
+alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var".
 
-inline cic:/CoRN/ftc/FTC/contF.var.
+alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var".
 
 (* UNEXPORTED
-Section Compact.
+Section Compact
 *)
 
 (*#*
@@ -202,60 +204,60 @@ continuous in [[a,b]], $x0\in[a,b]$#x0∈[a,b]#; denote by
 %\end{convention}%
 *)
 
-inline cic:/CoRN/ftc/FTC/a.var.
+alias id "a" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var".
 
-inline cic:/CoRN/ftc/FTC/b.var.
+alias id "b" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var".
 
-inline cic:/CoRN/ftc/FTC/Hab.var.
+alias id "Hab" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var".
 
-inline cic:/CoRN/ftc/FTC/contIf.var.
+alias id "contIf" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var".
 
-inline cic:/CoRN/ftc/FTC/contIF.var.
+alias id "contIF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var".
 
 (* begin show *)
 
-inline cic:/CoRN/ftc/FTC/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var".
 
 (* end show *)
 
-inline cic:/CoRN/ftc/FTC/x0.var.
+alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var".
 
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var".
 
-inline cic:/CoRN/ftc/FTC/Hx0'.var.
+alias id "Hx0'" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FTC/g.con.
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__".
 
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__".
 
 (* end hide *)
 
 (* begin show *)
 
-inline cic:/CoRN/ftc/FTC/contg.var.
+alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var".
 
-inline cic:/CoRN/ftc/FTC/contG.var.
+alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var".
 
 (* end show *)
 
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con".
 
 (* UNEXPORTED
-End Compact.
+End Compact
 *)
 
 (*#*
 And now we can generalize it step by step.
 *)
 
-inline cic:/CoRN/ftc/FTC/limit_of_integral.con.
+inline "cic:/CoRN/ftc/FTC/limit_of_integral.con".
 
-inline cic:/CoRN/ftc/FTC/limit_of_Integral.con.
+inline "cic:/CoRN/ftc/FTC/limit_of_Integral.con".
 
 (* UNEXPORTED
-Section General.
+Section General
 *)
 
 (*#*
@@ -264,38 +266,38 @@ Finally, with [x0, g, G] as before,
 
 (* begin show *)
 
-inline cic:/CoRN/ftc/FTC/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var".
 
 (* end show *)
 
-inline cic:/CoRN/ftc/FTC/x0.var.
+alias id "x0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var".
 
-inline cic:/CoRN/ftc/FTC/Hx0.var.
+alias id "Hx0" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var".
 
 (* begin hide *)
 
-inline cic:/CoRN/ftc/FTC/g.con.
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__".
 
-inline cic:/CoRN/ftc/FTC/G.con.
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__".
 
 (* end hide *)
 
-inline cic:/CoRN/ftc/FTC/contg.var.
+alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var".
 
-inline cic:/CoRN/ftc/FTC/contG.var.
+alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var".
 
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con".
 
 (* UNEXPORTED
-End General.
+End General
 *)
 
 (* UNEXPORTED
-End Limit_of_Integral_Seq.
+End Limit_of_Integral_Seq
 *)
 
 (* UNEXPORTED
-Section Limit_of_Derivative_Seq.
+Section Limit_of_Derivative_Seq
 *)
 
 (*#*
@@ -305,67 +307,67 @@ Similar results hold for the sequence of derivatives of a converging sequence; t
 %\end{convention}%
 *)
 
-inline cic:/CoRN/ftc/FTC/J.var.
+alias id "J" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var".
 
-inline cic:/CoRN/ftc/FTC/pJ.var.
+alias id "pJ" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var".
 
-inline cic:/CoRN/ftc/FTC/f.var.
+alias id "f" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var".
 
-inline cic:/CoRN/ftc/FTC/g.var.
+alias id "g" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var".
 
-inline cic:/CoRN/ftc/FTC/F.var.
+alias id "F" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var".
 
-inline cic:/CoRN/ftc/FTC/G.var.
+alias id "G" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var".
 
-inline cic:/CoRN/ftc/FTC/contf.var.
+alias id "contf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var".
 
-inline cic:/CoRN/ftc/FTC/contF.var.
+alias id "contF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var".
 
-inline cic:/CoRN/ftc/FTC/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var".
 
-inline cic:/CoRN/ftc/FTC/contg.var.
+alias id "contg" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var".
 
-inline cic:/CoRN/ftc/FTC/contG.var.
+alias id "contG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var".
 
-inline cic:/CoRN/ftc/FTC/convG.var.
+alias id "convG" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var".
 
-inline cic:/CoRN/ftc/FTC/derf.var.
+alias id "derf" = "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var".
 
-inline cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con.
+inline "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con".
 
 (* UNEXPORTED
-End Limit_of_Derivative_Seq.
+End Limit_of_Derivative_Seq
 *)
 
 (* UNEXPORTED
-Section Derivative_Series.
+Section Derivative_Series
 *)
 
 (*#*
 As a very important case of this result, we get a rule for deriving series.
 *)
 
-inline cic:/CoRN/ftc/FTC/J.var.
+alias id "J" = "cic:/CoRN/ftc/FTC/Derivative_Series/J.var".
 
-inline cic:/CoRN/ftc/FTC/pJ.var.
+alias id "pJ" = "cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var".
 
-inline cic:/CoRN/ftc/FTC/f.var.
+alias id "f" = "cic:/CoRN/ftc/FTC/Derivative_Series/f.var".
 
-inline cic:/CoRN/ftc/FTC/g.var.
+alias id "g" = "cic:/CoRN/ftc/FTC/Derivative_Series/g.var".
 
 (* begin show *)
 
-inline cic:/CoRN/ftc/FTC/convF.var.
+alias id "convF" = "cic:/CoRN/ftc/FTC/Derivative_Series/convF.var".
 
-inline cic:/CoRN/ftc/FTC/convG.var.
+alias id "convG" = "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var".
 
 (* end show *)
 
-inline cic:/CoRN/ftc/FTC/derF.var.
+alias id "derF" = "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var".
 
-inline cic:/CoRN/ftc/FTC/Derivative_FSeries.con.
+inline "cic:/CoRN/ftc/FTC/Derivative_FSeries.con".
 
 (* UNEXPORTED
-End Derivative_Series.
+End Derivative_Series
 *)