set "baseuri" "cic:/matita/CoRN-Decl/ftc/Rolle".
+include "CoRN.ma".
+
(* $Id: Rolle.v,v 1.6 2004/04/23 10:01:01 lcf Exp $ *)
-(* INCLUDE
-DiffTactics2
-*)
+include "tactics/DiffTactics2.ma".
-(* INCLUDE
-MoreFunctions
-*)
+include "ftc/MoreFunctions.ma".
(* UNEXPORTED
Section Rolle.
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
-inline cic:/CoRN/ftc/Rolle/I.con.
+inline "cic:/CoRN/ftc/Rolle/I.con".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
-inline cic:/CoRN/ftc/Rolle/derF.var.
+inline "cic:/CoRN/ftc/Rolle/derF.var".
-inline cic:/CoRN/ftc/Rolle/Ha.var.
+inline "cic:/CoRN/ftc/Rolle/Ha.var".
-inline cic:/CoRN/ftc/Rolle/Hb.var.
+inline "cic:/CoRN/ftc/Rolle/Hb.var".
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/Rolle/Fab.var.
+inline "cic:/CoRN/ftc/Rolle/Fab.var".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/e.var.
+inline "cic:/CoRN/ftc/Rolle/e.var".
-inline cic:/CoRN/ftc/Rolle/He.var.
+inline "cic:/CoRN/ftc/Rolle/He.var".
-inline cic:/CoRN/ftc/Rolle/contF'.con.
+inline "cic:/CoRN/ftc/Rolle/contF'.con".
-inline cic:/CoRN/ftc/Rolle/derivF.con.
+inline "cic:/CoRN/ftc/Rolle/derivF.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma2.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma2.con".
-inline cic:/CoRN/ftc/Rolle/df.con.
+inline "cic:/CoRN/ftc/Rolle/df.con".
-inline cic:/CoRN/ftc/Rolle/Hdf.con.
+inline "cic:/CoRN/ftc/Rolle/Hdf.con".
-inline cic:/CoRN/ftc/Rolle/Hf.con.
+inline "cic:/CoRN/ftc/Rolle/Hf.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma3.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma3.con".
-inline cic:/CoRN/ftc/Rolle/df'.con.
+inline "cic:/CoRN/ftc/Rolle/df'.con".
-inline cic:/CoRN/ftc/Rolle/Hdf'.con.
+inline "cic:/CoRN/ftc/Rolle/Hdf'.con".
-inline cic:/CoRN/ftc/Rolle/Hf'.con.
+inline "cic:/CoRN/ftc/Rolle/Hf'.con".
-inline cic:/CoRN/ftc/Rolle/d.con.
+inline "cic:/CoRN/ftc/Rolle/d.con".
-inline cic:/CoRN/ftc/Rolle/Hd.con.
+inline "cic:/CoRN/ftc/Rolle/Hd.con".
-inline cic:/CoRN/ftc/Rolle/incF.con.
+inline "cic:/CoRN/ftc/Rolle/incF.con".
-inline cic:/CoRN/ftc/Rolle/n.con.
+inline "cic:/CoRN/ftc/Rolle/n.con".
-inline cic:/CoRN/ftc/Rolle/fcp.con.
+inline "cic:/CoRN/ftc/Rolle/fcp.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma1.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma1.con".
-inline cic:/CoRN/ftc/Rolle/incF'.con.
+inline "cic:/CoRN/ftc/Rolle/incF'.con".
-inline cic:/CoRN/ftc/Rolle/fcp'.con.
+inline "cic:/CoRN/ftc/Rolle/fcp'.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma4.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma4.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma5.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma5.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma6.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma6.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma7.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma7.con".
-inline cic:/CoRN/ftc/Rolle/j.con.
+inline "cic:/CoRN/ftc/Rolle/j.con".
-inline cic:/CoRN/ftc/Rolle/Hj.con.
+inline "cic:/CoRN/ftc/Rolle/Hj.con".
-inline cic:/CoRN/ftc/Rolle/Hj'.con.
+inline "cic:/CoRN/ftc/Rolle/Hj'.con".
-inline cic:/CoRN/ftc/Rolle/k.con.
+inline "cic:/CoRN/ftc/Rolle/k.con".
-inline cic:/CoRN/ftc/Rolle/Hk.con.
+inline "cic:/CoRN/ftc/Rolle/Hk.con".
-inline cic:/CoRN/ftc/Rolle/Hk'.con.
+inline "cic:/CoRN/ftc/Rolle/Hk'.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma8.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma8.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma9.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma9.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma10.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma10.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma11.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma11.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma12.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma12.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma13.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma13.con".
-inline cic:/CoRN/ftc/Rolle/Rolle_lemma15.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle_lemma15.con".
(* end hide *)
-inline cic:/CoRN/ftc/Rolle/Rolle.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle.con".
(* UNEXPORTED
End Rolle.
The following is a simple corollary:
*)
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
-inline cic:/CoRN/ftc/Rolle/I.con.
+inline "cic:/CoRN/ftc/Rolle/I.con".
(* end hide *)
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
-inline cic:/CoRN/ftc/Rolle/HF.var.
+inline "cic:/CoRN/ftc/Rolle/HF.var".
(* begin show *)
-inline cic:/CoRN/ftc/Rolle/HA.var.
+inline "cic:/CoRN/ftc/Rolle/HA.var".
-inline cic:/CoRN/ftc/Rolle/HB.var.
+inline "cic:/CoRN/ftc/Rolle/HB.var".
(* end show *)
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con".
(* UNEXPORTED
End Law_of_the_Mean.
We can also state these theorems without expliciting the derivative of [F].
*)
-inline cic:/CoRN/ftc/Rolle/a.var.
+inline "cic:/CoRN/ftc/Rolle/a.var".
-inline cic:/CoRN/ftc/Rolle/b.var.
+inline "cic:/CoRN/ftc/Rolle/b.var".
-inline cic:/CoRN/ftc/Rolle/Hab'.var.
+inline "cic:/CoRN/ftc/Rolle/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/Hab.con.
+inline "cic:/CoRN/ftc/Rolle/Hab.con".
(* end hide *)
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
(* begin show *)
-inline cic:/CoRN/ftc/Rolle/HF.var.
+inline "cic:/CoRN/ftc/Rolle/HF.var".
(* end show *)
-inline cic:/CoRN/ftc/Rolle/Rolle'.con.
+inline "cic:/CoRN/ftc/Rolle/Rolle'.con".
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con".
(* UNEXPORTED
End Corollaries.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/Rolle/I.var.
+inline "cic:/CoRN/ftc/Rolle/I.var".
-inline cic:/CoRN/ftc/Rolle/pI.var.
+inline "cic:/CoRN/ftc/Rolle/pI.var".
-inline cic:/CoRN/ftc/Rolle/F.var.
+inline "cic:/CoRN/ftc/Rolle/F.var".
-inline cic:/CoRN/ftc/Rolle/F'.var.
+inline "cic:/CoRN/ftc/Rolle/F'.var".
(* begin show *)
-inline cic:/CoRN/ftc/Rolle/derF.var.
+inline "cic:/CoRN/ftc/Rolle/derF.var".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/Rolle/incF.con.
+inline "cic:/CoRN/ftc/Rolle/incF.con".
-inline cic:/CoRN/ftc/Rolle/incF'.con.
+inline "cic:/CoRN/ftc/Rolle/incF'.con".
(* end hide *)
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean.con".
(*#*
We further generalize the mean law by writing as an explicit bound.
*)
-inline cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con.
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con".
(* UNEXPORTED
End Generalizations.