set "baseuri" "cic:/matita/CoRN-Decl/ftc/Derivative".
+include "CoRN.ma".
+
(* $Id: Derivative.v,v 1.7 2004/04/23 10:00:58 lcf Exp $ *)
-(* INCLUDE
-Continuity
-*)
+include "ftc/Continuity.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Derivatives
%\end{convention}%
*)
-inline cic:/CoRN/ftc/Derivative/a.var.
+alias id "a" = "cic:/CoRN/ftc/Derivative/Definitions/a.var".
-inline cic:/CoRN/ftc/Derivative/b.var.
+alias id "b" = "cic:/CoRN/ftc/Derivative/Definitions/b.var".
-inline cic:/CoRN/ftc/Derivative/Hab'.var.
+alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Derivative/Hab.con.
+inline "cic:/CoRN/ftc/Derivative/Definitions/Hab.con" "Definitions__".
-inline cic:/CoRN/ftc/Derivative/I.con.
+inline "cic:/CoRN/ftc/Derivative/Definitions/I.con" "Definitions__".
(* end hide *)
-inline cic:/CoRN/ftc/Derivative/F.var.
+alias id "F" = "cic:/CoRN/ftc/Derivative/Definitions/F.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Derivative/P.con.
+inline "cic:/CoRN/ftc/Derivative/Definitions/P.con" "Definitions__".
(* end hide *)
-inline cic:/CoRN/ftc/Derivative/Derivative_I.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#* **Basic Properties
*)
-inline cic:/CoRN/ftc/Derivative/a.var.
+alias id "a" = "cic:/CoRN/ftc/Derivative/Basic_Properties/a.var".
-inline cic:/CoRN/ftc/Derivative/b.var.
+alias id "b" = "cic:/CoRN/ftc/Derivative/Basic_Properties/b.var".
-inline cic:/CoRN/ftc/Derivative/Hab'.var.
+alias id "Hab'" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Derivative/Hab.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab.con" "Basic_Properties__".
-inline cic:/CoRN/ftc/Derivative/I.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/I.con" "Basic_Properties__".
(* end hide *)
Like we did for equality, we begin by stating a lemma that makes proofs of derivation easier in practice.
*)
-inline cic:/CoRN/ftc/Derivative/Derivative_I_char.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_char.con".
(* end hide *)
Derivative is a well defined relation; we will make this explicit for both arguments:
*)
-inline cic:/CoRN/ftc/Derivative/F.var.
+alias id "F" = "cic:/CoRN/ftc/Derivative/Basic_Properties/F.var".
-inline cic:/CoRN/ftc/Derivative/G.var.
+alias id "G" = "cic:/CoRN/ftc/Derivative/Basic_Properties/G.var".
-inline cic:/CoRN/ftc/Derivative/H.var.
+alias id "H" = "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Derivative/P.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/P.con" "Basic_Properties__".
-inline cic:/CoRN/ftc/Derivative/Q.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Q.con" "Basic_Properties__".
-inline cic:/CoRN/ftc/Derivative/R.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/R.con" "Basic_Properties__".
(* end hide *)
-inline cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_wdl.con".
-inline cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_wdr.con".
(* begin hide *)
-inline cic:/CoRN/ftc/Derivative/Derivative_I_unique_lemma.con.
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Derivative_I_unique_lemma.con" "Basic_Properties__".
(* end hide *)
Derivative is unique.
*)
-inline cic:/CoRN/ftc/Derivative/Derivative_I_unique.con.
+inline "cic:/CoRN/ftc/Derivative/Derivative_I_unique.con".
(*#*
Finally, the set where we are considering the relation is included in the domain of both functions.
*)
-inline cic:/CoRN/ftc/Derivative/derivative_imp_inc.con.
+inline "cic:/CoRN/ftc/Derivative/derivative_imp_inc.con".
-inline cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con.
+inline "cic:/CoRN/ftc/Derivative/derivative_imp_inc'.con".
(*#*
Any function that is or has a derivative is continuous.
*)
-inline cic:/CoRN/ftc/Derivative/Hab''.var.
+alias id "Hab''" = "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var".
-inline cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con.
+inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin'_I.con".
-inline cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con.
+inline "cic:/CoRN/ftc/Derivative/deriv_imp_contin_I.con".
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(*#*
If [G] is the derivative of [F] in a given interval, then [G] is also the derivative of [F] in any smaller interval.
*)
-inline cic:/CoRN/ftc/Derivative/included_imp_deriv.con.
+inline "cic:/CoRN/ftc/Derivative/included_imp_deriv.con".