include "ftc/MoreFunctions.ma".
(* UNEXPORTED
-Section Rolle.
+Section Rolle
*)
(*#* *Rolle's Theorem
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/a.var".
+alias id "a" = "cic:/CoRN/ftc/Rolle/Rolle/a.var".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+alias id "b" = "cic:/CoRN/ftc/Rolle/Rolle/b.var".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var".
-inline "cic:/CoRN/ftc/Rolle/Hab.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hab.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/I.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/I.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/F.var".
+alias id "F" = "cic:/CoRN/ftc/Rolle/Rolle/F.var".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/Rolle/Rolle/F'.var".
-inline "cic:/CoRN/ftc/Rolle/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/Rolle/Rolle/derF.var".
-inline "cic:/CoRN/ftc/Rolle/Ha.var".
+alias id "Ha" = "cic:/CoRN/ftc/Rolle/Rolle/Ha.var".
-inline "cic:/CoRN/ftc/Rolle/Hb.var".
+alias id "Hb" = "cic:/CoRN/ftc/Rolle/Rolle/Hb.var".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/Fab.var".
+alias id "Fab" = "cic:/CoRN/ftc/Rolle/Rolle/Fab.var".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/e.var".
+alias id "e" = "cic:/CoRN/ftc/Rolle/Rolle/e.var".
-inline "cic:/CoRN/ftc/Rolle/He.var".
+alias id "He" = "cic:/CoRN/ftc/Rolle/Rolle/He.var".
-inline "cic:/CoRN/ftc/Rolle/contF'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/contF'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/derivF.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/derivF.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma2.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma2.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/df.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/df.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hdf.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hdf.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hf.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hf.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma3.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma3.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/df'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/df'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hdf'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hdf'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hf'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hf'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/d.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/d.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hd.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hd.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/incF.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/incF.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/n.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/n.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/fcp.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/fcp.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma1.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma1.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/incF'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/incF'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/fcp'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/fcp'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma4.con".
+(* NOTATION
+Notation cp := (compact_part a b Hab' d Hd).
+*)
+
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma4.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma5.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma5.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma6.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma6.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma7.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma7.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/j.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/j.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hj.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hj.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hj'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hj'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/k.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/k.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hk.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hk.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hk'.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hk'.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma8.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma8.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma9.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma9.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma10.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma10.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma11.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma11.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma12.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma12.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma13.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma13.con" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma15.con".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Rolle_lemma15.con" "Rolle__".
(* end hide *)
inline "cic:/CoRN/ftc/Rolle/Rolle.con".
(* UNEXPORTED
-End Rolle.
+End Rolle
*)
(* UNEXPORTED
-Section Law_of_the_Mean.
+Section Law_of_the_Mean
*)
(*#*
The following is a simple corollary:
*)
-inline "cic:/CoRN/ftc/Rolle/a.var".
+alias id "a" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+alias id "b" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/Hab.con".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab.con" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/I.con".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/I.con" "Law_of_the_Mean__".
(* end hide *)
-inline "cic:/CoRN/ftc/Rolle/F.var".
+alias id "F" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var".
-inline "cic:/CoRN/ftc/Rolle/HF.var".
+alias id "HF" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/HA.var".
+alias id "HA" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var".
-inline "cic:/CoRN/ftc/Rolle/HB.var".
+alias id "HB" = "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var".
(* end show *)
inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_I.con".
(* UNEXPORTED
-End Law_of_the_Mean.
+End Law_of_the_Mean
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
(*#*
We can also state these theorems without expliciting the derivative of [F].
*)
-inline "cic:/CoRN/ftc/Rolle/a.var".
+alias id "a" = "cic:/CoRN/ftc/Rolle/Corollaries/a.var".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+alias id "b" = "cic:/CoRN/ftc/Rolle/Corollaries/b.var".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+alias id "Hab'" = "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var".
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/Hab.con".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/Hab.con" "Corollaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/Rolle/F.var".
+alias id "F" = "cic:/CoRN/ftc/Rolle/Corollaries/F.var".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/HF.var".
+alias id "HF" = "cic:/CoRN/ftc/Rolle/Corollaries/HF.var".
(* end show *)
inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean'_I.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-Section Generalizations.
+Section Generalizations
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Rolle/I.var".
+alias id "I" = "cic:/CoRN/ftc/Rolle/Generalizations/I.var".
-inline "cic:/CoRN/ftc/Rolle/pI.var".
+alias id "pI" = "cic:/CoRN/ftc/Rolle/Generalizations/pI.var".
-inline "cic:/CoRN/ftc/Rolle/F.var".
+alias id "F" = "cic:/CoRN/ftc/Rolle/Generalizations/F.var".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+alias id "F'" = "cic:/CoRN/ftc/Rolle/Generalizations/F'.var".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/derF.var".
+alias id "derF" = "cic:/CoRN/ftc/Rolle/Generalizations/derF.var".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/incF.con".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/incF.con" "Generalizations__".
-inline "cic:/CoRN/ftc/Rolle/incF'.con".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/incF'.con" "Generalizations__".
(* end hide *)
inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean_ineq.con".
(* UNEXPORTED
-End Generalizations.
+End Generalizations
*)