set "baseuri" "cic:/matita/CoRN-Decl/ftc/Differentiability".
+include "CoRN.ma".
+
(* $Id: Differentiability.v,v 1.5 2004/04/20 22:38:49 hinderer Exp $ *)
-(* INCLUDE
-PartInterval
-*)
+include "ftc/PartInterval.ma".
-(* INCLUDE
-DerivativeOps
-*)
+include "ftc/DerivativeOps.ma".
(* UNEXPORTED
Section Definitions.
problems.
*)
-inline cic:/CoRN/ftc/Differentiability/Diffble_I.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I.con".
(* UNEXPORTED
End Definitions.
A function differentiable in [[a,b]] is differentiable in every proper compact subinterval of [[a,b]].
*)
-inline cic:/CoRN/ftc/Differentiability/included_imp_diffble.con.
+inline "cic:/CoRN/ftc/Differentiability/included_imp_diffble.con".
(*#*
A function differentiable in an interval is everywhere defined in that interval.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
(* end hide *)
-inline cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con.
+inline "cic:/CoRN/ftc/Differentiability/diffble_imp_inc.con".
(*#*
If a function has a derivative in an interval then it is differentiable in that interval.
*)
-inline cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con.
+inline "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con".
(* UNEXPORTED
End Local_Properties.
All the algebraic results carry on.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
(* end hide *)
Section Constants.
*)
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_const.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_id.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con".
(* UNEXPORTED
End Constants.
Section Well_Definedness.
*)
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/H.var.
+inline "cic:/CoRN/ftc/Differentiability/H.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con".
(* UNEXPORTED
End Well_Definedness.
*)
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/G.var.
+inline "cic:/CoRN/ftc/Differentiability/G.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/diffG.var.
+inline "cic:/CoRN/ftc/Differentiability/diffG.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_inv.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_mult.con".
(* begin show *)
-inline cic:/CoRN/ftc/Differentiability/Gbnd.var.
+inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
(* end show *)
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con".
(* UNEXPORTED
End Operations.
Section Corollaries.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
(* begin hide *)
-inline cic:/CoRN/ftc/Differentiability/Hab.con.
+inline "cic:/CoRN/ftc/Differentiability/Hab.con".
-inline cic:/CoRN/ftc/Differentiability/I.con.
+inline "cic:/CoRN/ftc/Differentiability/I.con".
(* end hide *)
-inline cic:/CoRN/ftc/Differentiability/F.var.
+inline "cic:/CoRN/ftc/Differentiability/F.var".
-inline cic:/CoRN/ftc/Differentiability/G.var.
+inline "cic:/CoRN/ftc/Differentiability/G.var".
-inline cic:/CoRN/ftc/Differentiability/diffF.var.
+inline "cic:/CoRN/ftc/Differentiability/diffF.var".
-inline cic:/CoRN/ftc/Differentiability/diffG.var.
+inline "cic:/CoRN/ftc/Differentiability/diffG.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_scal.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con".
-inline cic:/CoRN/ftc/Differentiability/Gbnd.var.
+inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_div.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con".
(* UNEXPORTED
End Corollaries.
induction using the constant and addition rules.
*)
-inline cic:/CoRN/ftc/Differentiability/a.var.
+inline "cic:/CoRN/ftc/Differentiability/a.var".
-inline cic:/CoRN/ftc/Differentiability/b.var.
+inline "cic:/CoRN/ftc/Differentiability/b.var".
-inline cic:/CoRN/ftc/Differentiability/Hab'.var.
+inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sumx.con".
-inline cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con.
+inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con".
(* UNEXPORTED
End Other_Properties.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con.
+inline "cic:/CoRN/ftc/Differentiability/diffble_imp_contin_I.con".
(* UNEXPORTED
Hint Immediate included_imp_contin deriv_imp_contin_I deriv_imp_contin'_I