set "baseuri" "cic:/matita/CoRN-Decl/ftc/DerivativeOps".
-include "CoRN_notation.ma".
+include "CoRN.ma".
(* $Id: DerivativeOps.v,v 1.3 2004/04/23 10:00:58 lcf Exp $ *)
include "ftc/Derivative.ma".
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* **Algebraic Operations
We begin with some technical stuff that will be necessary for division.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
+alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__".
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/P.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
+alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var".
(* end show *)
inline "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Local_Results.
+Section Local_Results
*)
(*#* **Local Results
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__".
(* end hide *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con".
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var".
-inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/G.var".
+alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var".
-inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
+alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var".
-inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
+alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con".
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
+alias id "Fbnd" = "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var".
(* end show *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con".
(* UNEXPORTED
-End Local_Results.
+End Local_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Corolaries.
+Section Corolaries
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+alias id "F" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var".
-inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/G.var".
+alias id "G" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var".
-inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
+alias id "G'" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var".
-inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var".
-inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
+alias id "derG" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var".
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con".
-inline "cic:/CoRN/ftc/DerivativeOps/Gbnd.var".
+alias id "Gbnd" = "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con".
(* UNEXPORTED
-End Corolaries.
+End Corolaries
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Derivative_Sums.
+Section Derivative_Sums
*)
(*#* The derivation rules for families of functions are easily proved by
induction using the constant and addition rules.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+alias id "a" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+alias id "b" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
+alias id "Hab" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__".
(* end hide *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con".
(* UNEXPORTED
-End Derivative_Sums.
+End Derivative_Sums
*)
(* UNEXPORTED