set "baseuri" "cic:/matita/CoRN-Decl/ftc/TaylorLemma".
+include "CoRN.ma".
+
(* $Id: TaylorLemma.v,v 1.8 2004/04/23 10:01:01 lcf Exp $ *)
-(* INCLUDE
-Rolle
-*)
+include "ftc/Rolle.ma".
(* UNEXPORTED
Opaque Min.
*)
(* UNEXPORTED
-Section Taylor_Defs.
+Section Taylor_Defs
*)
(*#* *Taylor's Theorem
[[Min(a,b),Max(a,b)]].
*)
-inline cic:/CoRN/ftc/TaylorLemma/a.var.
+alias id "a" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var".
-inline cic:/CoRN/ftc/TaylorLemma/b.var.
+alias id "b" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var".
-inline cic:/CoRN/ftc/TaylorLemma/Hap.var.
+alias id "Hap" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var".
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/Hab'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab'.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/Hab.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hab.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/I.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/I.con" "Taylor_Defs__".
(* end hide *)
-inline cic:/CoRN/ftc/TaylorLemma/F.var.
+alias id "F" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var".
-inline cic:/CoRN/ftc/TaylorLemma/Ha.var.
+alias id "Ha" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var".
-inline cic:/CoRN/ftc/TaylorLemma/Hb.var.
+alias id "Hb" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var".
(* begin show *)
-inline cic:/CoRN/ftc/TaylorLemma/fi.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/fi.con" "Taylor_Defs__".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma1.con".
(* end hide *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/TL_compact_a.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__".
+
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con.
+(* NOTATION
+Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a).
+*)
+
+(* NOTATION
+Notation B := (Build_subcsetoid_crr IR _ _ TL_compact_b).
+*)
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/TaylorLemma/funct_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i.con" "Taylor_Defs__".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/funct_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_i'.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/TL_a_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_b_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_x_i.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_a_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_b_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_x_i'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma2'.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma3'.con".
(* end hide *)
Taylor sum of order [n].
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_seq'.con".
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_seq'_aux.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Taylor_seq'_aux.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a.con".
(* end hide *)
It is easy to show that [b] is in the domain of this series, which allows us to write down the Taylor remainder around [b].
*)
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b.con".
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_a'.con".
-inline cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TL_lemma_b'.con".
(* end hide *)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_rem.con".
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/g.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g.con" "Taylor_Defs__".
(* UNEXPORTED
Opaque Taylor_seq'_aux Taylor_rem.
Opaque funct_i.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma4.con".
(* UNEXPORTED
Transparent funct_i funct_i'.
Opaque funct_i'.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma5.con".
(* UNEXPORTED
Transparent funct_i' FSumx.
*)
-inline cic:/CoRN/ftc/TaylorLemma/funct_aux.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/funct_aux.con" "Taylor_Defs__".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma6.con".
(* UNEXPORTED
Ltac Lazy_Included :=
| apply csf_wd_unfolded ]; Algebra.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma7.con".
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma8.con".
(* UNEXPORTED
Opaque funct_aux.
Transparent funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma9.con".
-inline cic:/CoRN/ftc/TaylorLemma/g'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/g'.con" "Taylor_Defs__".
(* UNEXPORTED
Opaque Taylor_rem funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma10.con".
(* UNEXPORTED
Transparent Taylor_rem funct_aux.
%\end{convention}%
*)
-inline cic:/CoRN/ftc/TaylorLemma/e.var.
+alias id "e" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var".
-inline cic:/CoRN/ftc/TaylorLemma/He.var.
+alias id "He" = "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var".
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma11.con".
(* end hide *)
(* begin show *)
-inline cic:/CoRN/ftc/TaylorLemma/deriv_Sn'.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/deriv_Sn'.con" "Taylor_Defs__".
(* end show *)
(* begin hide *)
-inline cic:/CoRN/ftc/TaylorLemma/TLH.con.
+inline "cic:/CoRN/ftc/TaylorLemma/TLH.con".
(* end hide *)
Transparent Taylor_rem funct_aux.
*)
-inline cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con.
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con".
(* UNEXPORTED
-End Taylor_Defs.
+End Taylor_Defs
*)