inline "cic:/CoRN/algebra/Basics/Zmult_absorb.con".
(* UNEXPORTED
-Section Well_foundedT.
+Section Well_foundedT
*)
-inline "cic:/CoRN/algebra/Basics/A.var".
+inline "cic:/CoRN/algebra/Basics/Well_foundedT/A.var" "Well_foundedT__".
-inline "cic:/CoRN/algebra/Basics/R.var".
+inline "cic:/CoRN/algebra/Basics/Well_foundedT/R.var" "Well_foundedT__".
(*#* The accessibility predicate is defined to be non-informative *)
inline "cic:/CoRN/algebra/Basics/Acc.ind".
(* UNEXPORTED
-End Well_foundedT.
+End Well_foundedT
*)
(* UNEXPORTED
-Section AccT.
+Section AccT
*)
-inline "cic:/CoRN/algebra/Basics/A.var".
+inline "cic:/CoRN/algebra/Basics/AccT/A.var" "AccT__".
inline "cic:/CoRN/algebra/Basics/well_founded.con".
(* UNEXPORTED
-End AccT.
+End AccT
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section IndT.
+Section IndT
*)
-inline "cic:/CoRN/algebra/Basics/A.var".
+inline "cic:/CoRN/algebra/Basics/IndT/A.var" "IndT__".
-inline "cic:/CoRN/algebra/Basics/R.var".
+inline "cic:/CoRN/algebra/Basics/IndT/R.var" "IndT__".
(* UNEXPORTED
-Section AccIter.
+Section AccIter
*)
-inline "cic:/CoRN/algebra/Basics/P.var".
+inline "cic:/CoRN/algebra/Basics/IndT/AccIter/P.var" "IndT__AccIter__".
-inline "cic:/CoRN/algebra/Basics/F.var".
+inline "cic:/CoRN/algebra/Basics/IndT/AccIter/F.var" "IndT__AccIter__".
inline "cic:/CoRN/algebra/Basics/Acc_inv.con".
inline "cic:/CoRN/algebra/Basics/Acc_iter.con".
(* UNEXPORTED
-End AccIter.
+End AccIter
*)
-inline "cic:/CoRN/algebra/Basics/Rwf.var".
+inline "cic:/CoRN/algebra/Basics/IndT/Rwf.var" "IndT__".
inline "cic:/CoRN/algebra/Basics/well_founded_induction_type.con".
(* UNEXPORTED
-End IndT.
+End IndT
*)
(* UNEXPORTED
-Section InductionT.
+Section InductionT
*)
-inline "cic:/CoRN/algebra/Basics/A.var".
+inline "cic:/CoRN/algebra/Basics/InductionT/A.var" "InductionT__".
-inline "cic:/CoRN/algebra/Basics/f.var".
+inline "cic:/CoRN/algebra/Basics/InductionT/f.var" "InductionT__".
inline "cic:/CoRN/algebra/Basics/ltof.con".
inline "cic:/CoRN/algebra/Basics/induction_ltof2T.con".
(* UNEXPORTED
-End InductionT.
+End InductionT
*)
(* UNEXPORTED
-Section InductionTT.
+Section InductionTT
*)
inline "cic:/CoRN/algebra/Basics/lt_wf_rect.con".
(* UNEXPORTED
-End InductionTT.
+End InductionTT
*)
include "algebra/CGroups.ma".
(* UNEXPORTED
-Section Abelian_Groups.
+Section Abelian_Groups
*)
(*#*
coercion cic:/matita/CoRN-Decl/algebra/CAbGroups/cag_crr.con 0 (* compounds *).
(* UNEXPORTED
-Section AbGroup_Axioms.
+Section AbGroup_Axioms
*)
-inline "cic:/CoRN/algebra/CAbGroups/G.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var" "Abelian_Groups__AbGroup_Axioms__".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
inline "cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con".
(* UNEXPORTED
-End AbGroup_Axioms.
+End AbGroup_Axioms
*)
(* UNEXPORTED
-Section SubCAbGroups.
+Section SubCAbGroups
*)
(*#*
** Subgroups of an Abelian Group
*)
-inline "cic:/CoRN/algebra/CAbGroups/G.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var" "Abelian_Groups__SubCAbGroups__".
-inline "cic:/CoRN/algebra/CAbGroups/P.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var" "Abelian_Groups__SubCAbGroups__".
-inline "cic:/CoRN/algebra/CAbGroups/Punit.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var" "Abelian_Groups__SubCAbGroups__".
-inline "cic:/CoRN/algebra/CAbGroups/op_pres_P.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var" "Abelian_Groups__SubCAbGroups__".
-inline "cic:/CoRN/algebra/CAbGroups/inv_pres_P.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var" "Abelian_Groups__SubCAbGroups__".
(*#*
%\begin{convention}%
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CAbGroups/subcrr.con".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/subcrr.con" "Abelian_Groups__SubCAbGroups__".
inline "cic:/CoRN/algebra/CAbGroups/isabgrp_scrr.con".
inline "cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.con".
(* UNEXPORTED
-End SubCAbGroups.
+End SubCAbGroups
*)
(* UNEXPORTED
-Section Various.
+Section Various
*)
(*#*
Hint Resolve cag_commutes_unfolded: algebra.
*)
-inline "cic:/CoRN/algebra/CAbGroups/G.var".
+inline "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var" "Abelian_Groups__Various__".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
inline "cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con".
(* UNEXPORTED
-End Various.
+End Various
*)
(* UNEXPORTED
-End Abelian_Groups.
+End Abelian_Groups
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Nice_Char.
+Section Nice_Char
*)
(*#*
function [inv] which inverts elements respective to [plus].
*)
-inline "cic:/CoRN/algebra/CAbGroups/S.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/unit.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/plus.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var" "Nice_Char__".
(*#*
%\begin{convention}%
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CAbGroups/plus_lext.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/plus_lunit.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/plus_comm.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/plus_assoc.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/inv.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var" "Nice_Char__".
-inline "cic:/CoRN/algebra/CAbGroups/inv_inv.var".
+inline "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var" "Nice_Char__".
inline "cic:/CoRN/algebra/CAbGroups/plus_rext.con".
inline "cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.con".
(* UNEXPORTED
-End Nice_Char.
+End Nice_Char
*)
(*#* ** Iteration
*)
(* UNEXPORTED
-Section Group_Extras.
+Section Group_Extras
*)
-inline "cic:/CoRN/algebra/CAbGroups/G.var".
+inline "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var" "Group_Extras__".
inline "cic:/CoRN/algebra/CAbGroups/nmult.con".
inline "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con".
(* UNEXPORTED
-End Group_Extras.
+End Group_Extras
*)
(* UNEXPORTED
include "algebra/CMonoids.ma".
(* UNEXPORTED
-Section Abelian_Monoids.
+Section Abelian_Monoids
*)
(*#*
coercion cic:/matita/CoRN-Decl/algebra/CAbMonoids/cam_crr.con 0 (* compounds *).
(* UNEXPORTED
-Section AbMonoid_Axioms.
+Section AbMonoid_Axioms
*)
-inline "cic:/CoRN/algebra/CAbMonoids/M.var".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/AbMonoid_Axioms/M.var" "Abelian_Monoids__AbMonoid_Axioms__".
(*#*
%\begin{convention}% Let [M] be an abelian monoid.
inline "cic:/CoRN/algebra/CAbMonoids/cam_commutes_unfolded.con".
(* UNEXPORTED
-End AbMonoid_Axioms.
+End AbMonoid_Axioms
*)
(* UNEXPORTED
-Section SubCAbMonoids.
+Section SubCAbMonoids
*)
(*#*
** Subgroups of an Abelian Monoid
*)
-inline "cic:/CoRN/algebra/CAbMonoids/M.var".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/M.var" "Abelian_Monoids__SubCAbMonoids__".
-inline "cic:/CoRN/algebra/CAbMonoids/P.var".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/P.var" "Abelian_Monoids__SubCAbMonoids__".
-inline "cic:/CoRN/algebra/CAbMonoids/Punit.var".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/Punit.var" "Abelian_Monoids__SubCAbMonoids__".
-inline "cic:/CoRN/algebra/CAbMonoids/op_pres_P.var".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/op_pres_P.var" "Abelian_Monoids__SubCAbMonoids__".
(*#*
%\begin{convention}%
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CAbMonoids/subcrr.con".
+inline "cic:/CoRN/algebra/CAbMonoids/Abelian_Monoids/SubCAbMonoids/subcrr.con" "Abelian_Monoids__SubCAbMonoids__".
inline "cic:/CoRN/algebra/CAbMonoids/isabgrp_scrr.con".
inline "cic:/CoRN/algebra/CAbMonoids/Build_SubCAbMonoid.con".
(* UNEXPORTED
-End SubCAbMonoids.
+End SubCAbMonoids
*)
(* UNEXPORTED
-End Abelian_Monoids.
+End Abelian_Monoids
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Field_axioms.
+Section Field_axioms
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Field_axioms/F.var" "Field_axioms__".
inline "cic:/CoRN/algebra/CFields/CField_is_CField.con".
inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse.con".
(* UNEXPORTED
-End Field_axioms.
+End Field_axioms
*)
(* UNEXPORTED
-Section Field_basics.
+Section Field_basics
*)
(*#* ** Field basics
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Field_basics/F.var" "Field_basics__".
inline "cic:/CoRN/algebra/CFields/rcpcl_is_inverse_unfolded.con".
inline "cic:/CoRN/algebra/CFields/field_mult_inv_op.con".
(* UNEXPORTED
-End Field_basics.
+End Field_basics
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Field_multiplication.
+Section Field_multiplication
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Field_multiplication/F.var" "Field_multiplication__".
inline "cic:/CoRN/algebra/CFields/mult_resp_ap_zero.con".
inline "cic:/CoRN/algebra/CFields/cond_square_eq.con".
(* UNEXPORTED
-End Field_multiplication.
+End Field_multiplication
*)
(* UNEXPORTED
-Section x_square.
+Section x_square
*)
inline "cic:/CoRN/algebra/CFields/x_xminone.con".
inline "cic:/CoRN/algebra/CFields/square_id.con".
(* UNEXPORTED
-End x_square.
+End x_square
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Rcpcl_properties.
+Section Rcpcl_properties
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Rcpcl_properties/F.var" "Rcpcl_properties__".
inline "cic:/CoRN/algebra/CFields/inv_one.con".
inline "cic:/CoRN/algebra/CFields/f_rcpcl_f_rcpcl.con".
(* UNEXPORTED
-End Rcpcl_properties.
+End Rcpcl_properties
*)
(* UNEXPORTED
-Section MultipGroup.
+Section MultipGroup
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/MultipGroup/F.var" "MultipGroup__".
(*#*
The multiplicative monoid of NonZeros.
inline "cic:/CoRN/algebra/CFields/cfield_to_mult_cgroup.con".
(* UNEXPORTED
-End MultipGroup.
+End MultipGroup
*)
(* UNEXPORTED
-Section Div_properties.
+Section Div_properties
*)
(*#*
%\end{nameconvention}%
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Div_properties/F.var" "Div_properties__".
inline "cic:/CoRN/algebra/CFields/div_prop.con".
inline "cic:/CoRN/algebra/CFields/div_strext.con".
(* UNEXPORTED
-End Div_properties.
+End Div_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Mult_Cancel_Ap_Zero.
+Section Mult_Cancel_Ap_Zero
*)
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/Mult_Cancel_Ap_Zero/F.var" "Mult_Cancel_Ap_Zero__".
inline "cic:/CoRN/algebra/CFields/mult_cancel_ap_zero_lft.con".
inline "cic:/CoRN/algebra/CFields/recip_resp_ap.con".
(* UNEXPORTED
-End Mult_Cancel_Ap_Zero.
+End Mult_Cancel_Ap_Zero
*)
(* UNEXPORTED
-Section CField_Ops.
+Section CField_Ops
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/X.var".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/X.var" "CField_Ops__".
-inline "cic:/CoRN/algebra/CFields/F.var".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/F.var" "CField_Ops__".
-inline "cic:/CoRN/algebra/CFields/G.var".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/G.var" "CField_Ops__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CFields/P.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/P.con" "CField_Ops__".
-inline "cic:/CoRN/algebra/CFields/Q.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/Q.con" "CField_Ops__".
(* end hide *)
(* UNEXPORTED
-Section Part_Function_Recip.
+Section Part_Function_Recip
*)
(*#*
Some auxiliary notions are helpful in defining the domain.
*)
-inline "cic:/CoRN/algebra/CFields/R.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/R.con" "CField_Ops__Part_Function_Recip__".
-inline "cic:/CoRN/algebra/CFields/Ext2R.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Recip/Ext2R.con" "CField_Ops__Part_Function_Recip__".
inline "cic:/CoRN/algebra/CFields/part_function_recip_strext.con".
inline "cic:/CoRN/algebra/CFields/Frecip.con".
(* UNEXPORTED
-End Part_Function_Recip.
+End Part_Function_Recip
*)
(* UNEXPORTED
-Section Part_Function_Div.
+Section Part_Function_Div
*)
(*#*
For division things work out almost in the same way.
*)
-inline "cic:/CoRN/algebra/CFields/R.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/R.con" "CField_Ops__Part_Function_Div__".
-inline "cic:/CoRN/algebra/CFields/Ext2R.con".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/Part_Function_Div/Ext2R.con" "CField_Ops__Part_Function_Div__".
inline "cic:/CoRN/algebra/CFields/part_function_div_strext.con".
inline "cic:/CoRN/algebra/CFields/Fdiv.con".
(* UNEXPORTED
-End Part_Function_Div.
+End Part_Function_Div
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CFields/R.var".
+inline "cic:/CoRN/algebra/CFields/CField_Ops/R.var" "CField_Ops__".
inline "cic:/CoRN/algebra/CFields/included_FRecip.con".
inline "cic:/CoRN/algebra/CFields/included_FDiv''.con".
(* UNEXPORTED
-End CField_Ops.
+End CField_Ops
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CGroup_axioms.
+Section CGroup_axioms
*)
-inline "cic:/CoRN/algebra/CGroups/G.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_axioms/G.var" "CGroup_axioms__".
inline "cic:/CoRN/algebra/CGroups/cg_inverse.con".
(* UNEXPORTED
-End CGroup_axioms.
+End CGroup_axioms
*)
(*#*
*)
(* UNEXPORTED
-Section CGroup_basics.
+Section CGroup_basics
*)
-inline "cic:/CoRN/algebra/CGroups/G.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/G.var" "CGroup_basics__".
inline "cic:/CoRN/algebra/CGroups/cg_rht_inv_unfolded.con".
*)
(* UNEXPORTED
-Section SubCGroups.
+Section SubCGroups
*)
-inline "cic:/CoRN/algebra/CGroups/P.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/P.var" "CGroup_basics__SubCGroups__".
-inline "cic:/CoRN/algebra/CGroups/Punit.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/Punit.var" "CGroup_basics__SubCGroups__".
-inline "cic:/CoRN/algebra/CGroups/op_pres_P.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/op_pres_P.var" "CGroup_basics__SubCGroups__".
-inline "cic:/CoRN/algebra/CGroups/inv_pres_P.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/inv_pres_P.var" "CGroup_basics__SubCGroups__".
-inline "cic:/CoRN/algebra/CGroups/subcrr.con".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subcrr.con" "CGroup_basics__SubCGroups__".
-inline "cic:/CoRN/algebra/CGroups/subinv.con".
+inline "cic:/CoRN/algebra/CGroups/CGroup_basics/SubCGroups/subinv.con" "CGroup_basics__SubCGroups__".
inline "cic:/CoRN/algebra/CGroups/isgrp_scrr.con".
inline "cic:/CoRN/algebra/CGroups/Build_SubCGroup.con".
(* UNEXPORTED
-End SubCGroups.
+End SubCGroups
*)
(* UNEXPORTED
-End CGroup_basics.
+End CGroup_basics
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Assoc_properties.
+Section Assoc_properties
*)
-inline "cic:/CoRN/algebra/CGroups/G.var".
+inline "cic:/CoRN/algebra/CGroups/Assoc_properties/G.var" "Assoc_properties__".
inline "cic:/CoRN/algebra/CGroups/assoc_2.con".
inline "cic:/CoRN/algebra/CGroups/plus_resp_eq.con".
(* UNEXPORTED
-End Assoc_properties.
+End Assoc_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section cgroups_apartness.
+Section cgroups_apartness
*)
-inline "cic:/CoRN/algebra/CGroups/G.var".
+inline "cic:/CoRN/algebra/CGroups/cgroups_apartness/G.var" "cgroups_apartness__".
inline "cic:/CoRN/algebra/CGroups/cg_add_ap_zero.con".
inline "cic:/CoRN/algebra/CGroups/minus_cancel_ap_rht.con".
(* UNEXPORTED
-End cgroups_apartness.
+End cgroups_apartness
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CGroup_Ops.
+Section CGroup_Ops
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CGroups/G.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/G.var" "CGroup_Ops__".
-inline "cic:/CoRN/algebra/CGroups/F.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/F.var" "CGroup_Ops__".
-inline "cic:/CoRN/algebra/CGroups/F'.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/F'.var" "CGroup_Ops__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CGroups/P.con".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/P.con" "CGroup_Ops__".
-inline "cic:/CoRN/algebra/CGroups/Q.con".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/Q.con" "CGroup_Ops__".
(* end hide *)
(* UNEXPORTED
-Section Part_Function_Inv.
+Section Part_Function_Inv
*)
inline "cic:/CoRN/algebra/CGroups/part_function_inv_strext.con".
inline "cic:/CoRN/algebra/CGroups/Finv.con".
(* UNEXPORTED
-End Part_Function_Inv.
+End Part_Function_Inv
*)
(* UNEXPORTED
-Section Part_Function_Minus.
+Section Part_Function_Minus
*)
inline "cic:/CoRN/algebra/CGroups/part_function_minus_strext.con".
inline "cic:/CoRN/algebra/CGroups/Fminus.con".
(* UNEXPORTED
-End Part_Function_Minus.
+End Part_Function_Minus
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CGroups/R.var".
+inline "cic:/CoRN/algebra/CGroups/CGroup_Ops/R.var" "CGroup_Ops__".
inline "cic:/CoRN/algebra/CGroups/included_FInv.con".
inline "cic:/CoRN/algebra/CGroups/included_FMinus''.con".
(* UNEXPORTED
-End CGroup_Ops.
+End CGroup_Ops
*)
(* UNEXPORTED
inline "cic:/CoRN/algebra/CLogic/CProp.con".
(* UNEXPORTED
-Section Basics.
+Section Basics
*)
(*#* ** Basics
*)
(* UNEXPORTED
-End Basics.
+End Basics
*)
(* begin hide *)
*)
(* UNEXPORTED
-Section Choice.
+Section Choice
*)
(* **Choice
Let [P] be a predicate on $\NN^2$#N times N#.
*)
-inline "cic:/CoRN/algebra/CLogic/P.var".
+inline "cic:/CoRN/algebra/CLogic/Choice/P.var" "Choice__".
inline "cic:/CoRN/algebra/CLogic/choice.con".
(* UNEXPORTED
-End Choice.
+End Choice
*)
(* UNEXPORTED
-Section Logical_Remarks.
+Section Logical_Remarks
*)
(*#* We prove a few logical results which are helpful to have as lemmas
inline "cic:/CoRN/algebra/CLogic/CdeMorgan_ex_all.con".
(* UNEXPORTED
-End Logical_Remarks.
+End Logical_Remarks
*)
(* UNEXPORTED
-Section CRelation_Definition.
+Section CRelation_Definition
*)
(*#* ** [CProp]-valued Relations
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CLogic/A.var".
+inline "cic:/CoRN/algebra/CLogic/CRelation_Definition/A.var" "CRelation_Definition__".
inline "cic:/CoRN/algebra/CLogic/Crelation.con".
-inline "cic:/CoRN/algebra/CLogic/R.var".
+inline "cic:/CoRN/algebra/CLogic/CRelation_Definition/R.var" "CRelation_Definition__".
inline "cic:/CoRN/algebra/CLogic/Creflexive.con".
inline "cic:/CoRN/algebra/CLogic/Cequiv.con".
(* UNEXPORTED
-End CRelation_Definition.
+End CRelation_Definition
*)
(* UNEXPORTED
-Section TRelation_Definition.
+Section TRelation_Definition
*)
(*#* ** [Prop]-valued Relations
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CLogic/A.var".
+inline "cic:/CoRN/algebra/CLogic/TRelation_Definition/A.var" "TRelation_Definition__".
inline "cic:/CoRN/algebra/CLogic/Trelation.con".
-inline "cic:/CoRN/algebra/CLogic/R.var".
+inline "cic:/CoRN/algebra/CLogic/TRelation_Definition/R.var" "TRelation_Definition__".
inline "cic:/CoRN/algebra/CLogic/Treflexive.con".
inline "cic:/CoRN/algebra/CLogic/Tequiv.con".
(* UNEXPORTED
-End TRelation_Definition.
+End TRelation_Definition
*)
inline "cic:/CoRN/algebra/CLogic/eqs.ind".
(* UNEXPORTED
-Section le_odd.
+Section le_odd
*)
(*#* ** The relation [le], [lt], [odd] and [even] in [CProp]
inline "cic:/CoRN/algebra/CLogic/to_Ceven.con".
(* UNEXPORTED
-End le_odd.
+End le_odd
*)
(* UNEXPORTED
-Section Misc.
+Section Misc
*)
(*#* **Miscellaneous
inline "cic:/CoRN/algebra/CLogic/not_l_sum_rec.con".
(* UNEXPORTED
-End Misc.
+End Misc
*)
(*#* **Results about the natural numbers
*)
(* UNEXPORTED
-Section Odd_and_Even.
+Section Odd_and_Even
*)
(*#*
inline "cic:/CoRN/algebra/CLogic/even_or_odd_plus_gt.con".
(* UNEXPORTED
-End Odd_and_Even.
+End Odd_and_Even
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Natural_Numbers.
+Section Natural_Numbers
*)
(*#* **Algebraic Properties
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CLogic/h.var".
+inline "cic:/CoRN/algebra/CLogic/Natural_Numbers/h.var" "Natural_Numbers__".
(*#*
First we characterize monotonicity by a local condition: if [h(n) < h(n+1)]
inline "cic:/CoRN/algebra/CLogic/weird_mon_covers.con".
(* UNEXPORTED
-End Natural_Numbers.
+End Natural_Numbers
*)
(*#*
inline "cic:/CoRN/algebra/CLogic/kseq_prop.con".
(* UNEXPORTED
-Section Predicates_to_CProp.
+Section Predicates_to_CProp
*)
(*#* **Logical Properties
inline "cic:/CoRN/algebra/CLogic/str_finite_or_elim.con".
(* UNEXPORTED
-End Predicates_to_CProp.
+End Predicates_to_CProp
*)
(* UNEXPORTED
-Section Predicates_to_Prop.
+Section Predicates_to_Prop
*)
(*#* Finally, analogous results for [Prop]-valued predicates are presented for
inline "cic:/CoRN/algebra/CLogic/four_ind.con".
(* UNEXPORTED
-End Predicates_to_Prop.
+End Predicates_to_Prop
*)
(*#* **Integers
*)
(* UNEXPORTED
-Section CMonoid_axioms.
+Section CMonoid_axioms
*)
-inline "cic:/CoRN/algebra/CMonoids/M.var".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_axioms/M.var" "CMonoid_axioms__".
inline "cic:/CoRN/algebra/CMonoids/CMonoid_is_CMonoid.con".
inline "cic:/CoRN/algebra/CMonoids/cm_lft_unit.con".
(* UNEXPORTED
-End CMonoid_axioms.
+End CMonoid_axioms
*)
(*#*
*)
(* UNEXPORTED
-Section CMonoid_basics.
+Section CMonoid_basics
*)
-inline "cic:/CoRN/algebra/CMonoids/M.var".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/M.var" "CMonoid_basics__".
inline "cic:/CoRN/algebra/CMonoids/cm_rht_unit_unfolded.con".
*)
(* UNEXPORTED
-Section SubCMonoids.
+Section SubCMonoids
*)
-inline "cic:/CoRN/algebra/CMonoids/P.var".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/P.var" "CMonoid_basics__SubCMonoids__".
-inline "cic:/CoRN/algebra/CMonoids/Punit.var".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/Punit.var" "CMonoid_basics__SubCMonoids__".
-inline "cic:/CoRN/algebra/CMonoids/op_pres_P.var".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/op_pres_P.var" "CMonoid_basics__SubCMonoids__".
-inline "cic:/CoRN/algebra/CMonoids/subcrr.con".
+inline "cic:/CoRN/algebra/CMonoids/CMonoid_basics/SubCMonoids/subcrr.con" "CMonoid_basics__SubCMonoids__".
inline "cic:/CoRN/algebra/CMonoids/ismon_scrr.con".
inline "cic:/CoRN/algebra/CMonoids/Build_SubCMonoid.con".
(* UNEXPORTED
-End SubCMonoids.
+End SubCMonoids
*)
(* UNEXPORTED
-End CMonoid_basics.
+End CMonoid_basics
*)
(* UNEXPORTED
(* End_SpecReals *)
(* UNEXPORTED
-Section AbsSmall_properties.
+Section AbsSmall_properties
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdAbs/R.var".
+inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_properties/R.var" "AbsSmall_properties__".
inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_wdr.con".
inline "cic:/CoRN/algebra/COrdAbs/AbsSmall_approach_zero.con".
(* UNEXPORTED
-End AbsSmall_properties.
+End AbsSmall_properties
*)
(* UNEXPORTED
inline "cic:/CoRN/algebra/COrdAbs/AbsBigSmall_minus.con".
(* UNEXPORTED
-Section absBig_wd_properties.
+Section absBig_wd_properties
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdAbs/R.var".
+inline "cic:/CoRN/algebra/COrdAbs/absBig_wd_properties/R.var" "absBig_wd_properties__".
inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdr.con".
inline "cic:/CoRN/algebra/COrdAbs/AbsBig_wdl_unfolded.con".
(* UNEXPORTED
-End absBig_wd_properties.
+End absBig_wd_properties
*)
(* UNEXPORTED
(* Begin_SpecReals *)
(* UNEXPORTED
-Section OrdField_Cauchy.
+Section OrdField_Cauchy
*)
(*#* **Cauchy sequences
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdCauchy/R.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/R.var" "OrdField_Cauchy__".
(* begin hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdCauchy/f.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/g.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/g.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/Hf.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hf.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/Hg.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/Hg.var" "OrdField_Cauchy__".
inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_plus.con".
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdCauchy/e.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/e.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/He.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/He.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/N.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/N.var" "OrdField_Cauchy__".
-inline "cic:/CoRN/algebra/COrdCauchy/f_bnd.var".
+inline "cic:/CoRN/algebra/COrdCauchy/OrdField_Cauchy/f_bnd.var" "OrdField_Cauchy__".
inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip_def.con".
inline "cic:/CoRN/algebra/COrdCauchy/CS_seq_recip.con".
(* UNEXPORTED
-End OrdField_Cauchy.
+End OrdField_Cauchy
*)
(* UNEXPORTED
inline "cic:/CoRN/algebra/COrdCauchy/maj_upto_eps.con".
(* UNEXPORTED
-Section Mult_AbsSmall.
+Section Mult_AbsSmall
*)
-inline "cic:/CoRN/algebra/COrdCauchy/R.var".
+inline "cic:/CoRN/algebra/COrdCauchy/Mult_AbsSmall/R.var" "Mult_AbsSmall__".
(*#*
** [AbsSmall] revisited
inline "cic:/CoRN/algebra/COrdCauchy/mult_AbsSmall.con".
(* UNEXPORTED
-End Mult_AbsSmall.
+End Mult_AbsSmall
*)
(* UNEXPORTED
-Section Mult_Continuous.
+Section Mult_Continuous
*)
-inline "cic:/CoRN/algebra/COrdCauchy/R.var".
+inline "cic:/CoRN/algebra/COrdCauchy/Mult_Continuous/R.var" "Mult_Continuous__".
(*#*
** Multiplication is continuous
inline "cic:/CoRN/algebra/COrdCauchy/plus_contin.con".
(* UNEXPORTED
-End Mult_Continuous.
+End Mult_Continuous
*)
(* UNEXPORTED
-Section Monotonous_functions.
+Section Monotonous_functions
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdCauchy/R.var".
+inline "cic:/CoRN/algebra/COrdCauchy/Monotonous_functions/R.var" "Monotonous_functions__".
(*#*
We begin by characterizing the preservation of less (less or equal)
inline "cic:/CoRN/algebra/COrdCauchy/part_mon_imp_mon'.con".
(* UNEXPORTED
-End Monotonous_functions.
+End Monotonous_functions
*)
*)
(* UNEXPORTED
-Section COrdField_axioms.
+Section COrdField_axioms
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdFields/F.var".
+inline "cic:/CoRN/algebra/COrdFields/COrdField_axioms/F.var" "COrdField_axioms__".
inline "cic:/CoRN/algebra/COrdFields/COrdField_is_COrdField.con".
inline "cic:/CoRN/algebra/COrdFields/less_wdl.con".
(* UNEXPORTED
-End COrdField_axioms.
+End COrdField_axioms
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section OrdField_basics.
+Section OrdField_basics
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdFields/R.var".
+inline "cic:/CoRN/algebra/COrdFields/OrdField_basics/R.var" "OrdField_basics__".
inline "cic:/CoRN/algebra/COrdFields/less_imp_ap.con".
inline "cic:/CoRN/algebra/COrdFields/leEq_not_eq.con".
(* UNEXPORTED
-End OrdField_basics.
+End OrdField_basics
*)
(*#**********************************)
(* UNEXPORTED
-Section Basic_Properties_of_leEq.
+Section Basic_Properties_of_leEq
*)
(*#**********************************)
(*#* ** Basic properties of [ [<=] ]
*)
-inline "cic:/CoRN/algebra/COrdFields/R.var".
+inline "cic:/CoRN/algebra/COrdFields/Basic_Properties_of_leEq/R.var" "Basic_Properties_of_leEq__".
inline "cic:/CoRN/algebra/COrdFields/leEq_wdr.con".
inline "cic:/CoRN/algebra/COrdFields/less_leEq.con".
(* UNEXPORTED
-End Basic_Properties_of_leEq.
+End Basic_Properties_of_leEq
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section infinity_of_cordfields.
+Section infinity_of_cordfields
*)
(*#*
e.g.%\% [x[/]TwoNZ].
*)
-inline "cic:/CoRN/algebra/COrdFields/R.var".
+inline "cic:/CoRN/algebra/COrdFields/infinity_of_cordfields/R.var" "infinity_of_cordfields__".
inline "cic:/CoRN/algebra/COrdFields/pos_one.con".
include "tactics/Opaque_algebra.ma".
(* UNEXPORTED
-Section up_to_four.
+Section up_to_four
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields/four_ap_zero.con".
(* UNEXPORTED
-End up_to_four.
+End up_to_four
*)
(* UNEXPORTED
-Section More_than_four.
+Section More_than_four
*)
(*#* *** Properties of some other numbers *)
inline "cic:/CoRN/algebra/COrdFields/fortyeight_ap_zero.con".
(* UNEXPORTED
-End More_than_four.
+End More_than_four
*)
(* UNEXPORTED
-End infinity_of_cordfields.
+End infinity_of_cordfields
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section consequences_of_infinity.
+Section consequences_of_infinity
*)
(*#*
*** Consequences of infinity
*)
-inline "cic:/CoRN/algebra/COrdFields/F.var".
+inline "cic:/CoRN/algebra/COrdFields/consequences_of_infinity/F.var" "consequences_of_infinity__".
inline "cic:/CoRN/algebra/COrdFields/square_eq.con".
inline "cic:/CoRN/algebra/COrdFields/char0_OrdField.con".
(* UNEXPORTED
-End consequences_of_infinity.
+End consequences_of_infinity
*)
(*#**********************************)
(* UNEXPORTED
-Section Properties_of_Ordering.
+Section Properties_of_Ordering
*)
(*#**********************************)
** Properties of [[<]]
*)
-inline "cic:/CoRN/algebra/COrdFields/R.var".
+inline "cic:/CoRN/algebra/COrdFields/Properties_of_Ordering/R.var" "Properties_of_Ordering__".
(*#*
We do not use a special predicate for positivity,
*)
(* UNEXPORTED
-Section addition.
+Section addition
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields/qltone.con".
(* UNEXPORTED
-End addition.
+End addition
*)
(* UNEXPORTED
-Section multiplication.
+Section multiplication
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields/pos_div_fortyeight.con".
(* UNEXPORTED
-End multiplication.
+End multiplication
*)
(* UNEXPORTED
-Section misc.
+Section misc
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields/negative_Sumx.con".
(* UNEXPORTED
-End misc.
+End misc
*)
(* UNEXPORTED
-End Properties_of_Ordering.
+End Properties_of_Ordering
*)
(*#**********************************)
(* UNEXPORTED
-Section Properties_of_leEq.
+Section Properties_of_leEq
*)
(*#**********************************)
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdFields2/R.var".
+inline "cic:/CoRN/algebra/COrdFields2/Properties_of_leEq/R.var" "Properties_of_leEq__".
(* UNEXPORTED
-Section addition.
+Section addition
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields2/shift_zero_leEq_minus'.con".
(* UNEXPORTED
-End addition.
+End addition
*)
(* UNEXPORTED
-Section multiplication.
+Section multiplication
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields2/nonneg_div_four'.con".
(* UNEXPORTED
-End multiplication.
+End multiplication
*)
(* UNEXPORTED
-Section misc.
+Section misc
*)
(*#*
inline "cic:/CoRN/algebra/COrdFields2/approach_zero_weak.con".
(* UNEXPORTED
-End misc.
+End misc
*)
inline "cic:/CoRN/algebra/COrdFields2/equal_less_leEq.con".
(* UNEXPORTED
-End Properties_of_leEq.
+End Properties_of_leEq
*)
(*#**********************************)
(* UNEXPORTED
-Section PosP_properties.
+Section PosP_properties
*)
(*#**********************************)
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdFields2/R.var".
+inline "cic:/CoRN/algebra/COrdFields2/PosP_properties/R.var" "PosP_properties__".
(* begin hide *)
inline "cic:/CoRN/algebra/COrdFields2/square_eq_neg.con".
(* UNEXPORTED
-End PosP_properties.
+End PosP_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section One_div_succ_properties.
+Section One_div_succ_properties
*)
-inline "cic:/CoRN/algebra/COrdFields2/R.var".
+inline "cic:/CoRN/algebra/COrdFields2/One_div_succ_properties/R.var" "One_div_succ_properties__".
inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_leEq.con".
inline "cic:/CoRN/algebra/COrdFields2/one_div_succ_resp_less.con".
(* UNEXPORTED
-End One_div_succ_properties.
+End One_div_succ_properties
*)
(*#*
*)
(* UNEXPORTED
-Section Half_properties.
+Section Half_properties
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/COrdFields2/R.var".
+inline "cic:/CoRN/algebra/COrdFields2/Half_properties/R.var" "Half_properties__".
inline "cic:/CoRN/algebra/COrdFields2/half_1.con".
inline "cic:/CoRN/algebra/COrdFields2/half_3.con".
(* UNEXPORTED
-End Half_properties.
+End Half_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Poly_Representation.
+Section Poly_Representation
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/R.var" "Poly_Representation__".
-inline "cic:/CoRN/algebra/CPoly_ApZero/a_.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/a_.var" "Poly_Representation__".
-inline "cic:/CoRN/algebra/CPoly_ApZero/distinct_a_.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/distinct_a_.var" "Poly_Representation__".
-inline "cic:/CoRN/algebra/CPoly_ApZero/f.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/f.var" "Poly_Representation__".
-inline "cic:/CoRN/algebra/CPoly_ApZero/n.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/n.var" "Poly_Representation__".
-inline "cic:/CoRN/algebra/CPoly_ApZero/degree_f.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_Representation/degree_f.var" "Poly_Representation__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_choose_apzero.con".
(* UNEXPORTED
-End Poly_Representation.
+End Poly_Representation
*)
(* UNEXPORTED
-Section Characteristic_zero.
+Section Characteristic_zero
*)
(*#*
strengthened.
*)
-inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/R.var" "Characteristic_zero__".
(* begin show *)
-inline "cic:/CoRN/algebra/CPoly_ApZero/H.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Characteristic_zero/H.var" "Characteristic_zero__".
(* end show *)
inline "cic:/CoRN/algebra/CPoly_ApZero/poly_extensional.con".
(* UNEXPORTED
-End Characteristic_zero.
+End Characteristic_zero
*)
(*#*
*)
(* UNEXPORTED
-Section Poly_ApZero_Interval.
+Section Poly_ApZero_Interval
*)
-inline "cic:/CoRN/algebra/CPoly_ApZero/R.var".
+inline "cic:/CoRN/algebra/CPoly_ApZero/Poly_ApZero_Interval/R.var" "Poly_ApZero_Interval__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_ApZero/Cpoly_apzero_interval.con".
(* UNEXPORTED
-End Poly_ApZero_Interval.
+End Poly_ApZero_Interval
*)
*)
(* UNEXPORTED
-Section Degree_def.
+Section Degree_def
*)
-inline "cic:/CoRN/algebra/CPoly_Degree/R.var".
+inline "cic:/CoRN/algebra/CPoly_Degree/Degree_def/R.var" "Degree_def__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_Degree/regular.con".
(* UNEXPORTED
-End Degree_def.
+End Degree_def
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Degree_props.
+Section Degree_props
*)
-inline "cic:/CoRN/algebra/CPoly_Degree/R.var".
+inline "cic:/CoRN/algebra/CPoly_Degree/Degree_props/R.var" "Degree_props__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_Degree/monic_apzero.con".
(* UNEXPORTED
-End Degree_props.
+End Degree_props
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section degree_props_Field.
+Section degree_props_Field
*)
(*#* ** Degrees of polynomials over a field
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CPoly_Degree/F.var".
+inline "cic:/CoRN/algebra/CPoly_Degree/degree_props_Field/F.var" "degree_props_Field__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_Degree/degree_mult_imp.con".
(* UNEXPORTED
-End degree_props_Field.
+End degree_props_Field
*)
*)
(* UNEXPORTED
-Section NthCoeff_def.
+Section NthCoeff_def
*)
-inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var".
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_def/R.var" "NthCoeff_def__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_S.con".
(* UNEXPORTED
-End NthCoeff_def.
+End NthCoeff_def
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section NthCoeff_props.
+Section NthCoeff_props
*)
(*#* ** Properties of [nth_coeff] *)
-inline "cic:/CoRN/algebra/CPoly_NthCoeff/R.var".
+inline "cic:/CoRN/algebra/CPoly_NthCoeff/NthCoeff_props/R.var" "NthCoeff_props__".
(* begin hide *)
inline "cic:/CoRN/algebra/CPoly_NthCoeff/nth_coeff_mult.con".
(* UNEXPORTED
-End NthCoeff_props.
+End NthCoeff_props
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CPoly_CRing.
+Section CPoly_CRing
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CPolynomials/CR.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/CR.var" "CPoly_CRing__".
(*#*
The intuition behind the type [cpoly] is the following
in terms of these generators.
*)
-inline "cic:/CoRN/algebra/CPolynomials/cpoly_zero_cs.con".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_zero_cs.con" "CPoly_CRing__".
-inline "cic:/CoRN/algebra/CPolynomials/cpoly_linear_cs.con".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing/cpoly_linear_cs.con" "CPoly_CRing__".
inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_ind_cs.con".
inline "cic:/CoRN/algebra/CPolynomials/cpoly_x_minus_c_wd.con".
(* UNEXPORTED
-End CPoly_CRing.
+End CPoly_CRing
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CPoly_CRing_ctd.
+Section CPoly_CRing_ctd
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CPolynomials/CR.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/CR.var" "CPoly_CRing_ctd__".
(* NOTATION
Notation RX := (cpoly_cring CR).
*)
(* UNEXPORTED
-Section helpful_section.
+Section helpful_section
*)
-inline "cic:/CoRN/algebra/CPolynomials/p.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/p.var" "CPoly_CRing_ctd__helpful_section__".
-inline "cic:/CoRN/algebra/CPolynomials/q.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/q.var" "CPoly_CRing_ctd__helpful_section__".
-inline "cic:/CoRN/algebra/CPolynomials/c.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/c.var" "CPoly_CRing_ctd__helpful_section__".
-inline "cic:/CoRN/algebra/CPolynomials/d.var".
+inline "cic:/CoRN/algebra/CPolynomials/CPoly_CRing_ctd/helpful_section/d.var" "CPoly_CRing_ctd__helpful_section__".
inline "cic:/CoRN/algebra/CPolynomials/linear_eq_zero_.con".
inline "cic:/CoRN/algebra/CPolynomials/linear_ap_linear.con".
(* UNEXPORTED
-End helpful_section.
+End helpful_section
*)
inline "cic:/CoRN/algebra/CPolynomials/Ccpoly_induc.con".
inline "cic:/CoRN/algebra/CPolynomials/cpoly_apply_fun.con".
(* UNEXPORTED
-End CPoly_CRing_ctd.
+End CPoly_CRing_ctd
*)
(*#*
*)
(* UNEXPORTED
-Section Poly_properties.
+Section Poly_properties
*)
-inline "cic:/CoRN/algebra/CPolynomials/R.var".
+inline "cic:/CoRN/algebra/CPolynomials/Poly_properties/R.var" "Poly_properties__".
(* NOTATION
Notation RX := (cpoly_cring R).
inline "cic:/CoRN/algebra/CPolynomials/Sum_cpoly_ap.con".
(* UNEXPORTED
-End Poly_properties.
+End Poly_properties
*)
(*#* ** Induction properties of polynomials for [Prop]
*)
(* UNEXPORTED
-Section Poly_Prop_Induction.
+Section Poly_Prop_Induction
*)
-inline "cic:/CoRN/algebra/CPolynomials/CR.var".
+inline "cic:/CoRN/algebra/CPolynomials/Poly_Prop_Induction/CR.var" "Poly_Prop_Induction__".
(* NOTATION
Notation Cpoly := (cpoly CR).
inline "cic:/CoRN/algebra/CPolynomials/cpoly_double_ind.con".
(* UNEXPORTED
-End Poly_Prop_Induction.
+End Poly_Prop_Induction
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CRing_axioms.
+Section CRing_axioms
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/CRing_axioms/R.var" "CRing_axioms__".
inline "cic:/CoRN/algebra/CRings/CRing_is_CRing.con".
(* Begin_SpecReals *)
(* UNEXPORTED
-End CRing_axioms.
+End CRing_axioms
*)
(* UNEXPORTED
-Section Ring_constructions.
+Section Ring_constructions
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_constructions/R.var" "Ring_constructions__".
(*#*
The multiplicative monoid of a ring is defined as follows.
inline "cic:/CoRN/algebra/CRings/Build_multCMonoid.con".
(* UNEXPORTED
-End Ring_constructions.
+End Ring_constructions
*)
(* End_SpecReals *)
(* UNEXPORTED
-Section Ring_unfolded.
+Section Ring_unfolded
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_unfolded/R.var" "Ring_unfolded__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CRings/mmR.con".
+inline "cic:/CoRN/algebra/CRings/Ring_unfolded/mmR.con" "Ring_unfolded__".
(* end hide *)
inline "cic:/CoRN/algebra/CRings/ring_distl_unfolded.con".
(* UNEXPORTED
-End Ring_unfolded.
+End Ring_unfolded
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Ring_basics.
+Section Ring_basics
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_basics/R.var" "Ring_basics__".
inline "cic:/CoRN/algebra/CRings/one_ap_zero.con".
*)
(* UNEXPORTED
-End Ring_basics.
+End Ring_basics
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section exponentiation.
+Section exponentiation
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/exponentiation/R.var" "exponentiation__".
(* End_SpecReals *)
(* Begin_SpecReals *)
(* UNEXPORTED
-End exponentiation.
+End exponentiation
*)
(* End_SpecReals *)
(* Begin_SpecReals *)
(* UNEXPORTED
-Section nat_injection.
+Section nat_injection
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/nat_injection/R.var" "nat_injection__".
(*#*
The injection of Coq natural numbers into a ring is called [nring].
(* Begin_SpecReals *)
(* UNEXPORTED
-End nat_injection.
+End nat_injection
*)
(* End_SpecReals *)
inline "cic:/CoRN/algebra/CRings/nring_different.con".
(* UNEXPORTED
-Section int_injection.
+Section int_injection
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/int_injection/R.var" "int_injection__".
(*#*
The injection of Coq integers into a ring is called [zring]. Again,
inline "cic:/CoRN/algebra/CRings/zring_inv_one.con".
(* UNEXPORTED
-End int_injection.
+End int_injection
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Ring_sums.
+Section Ring_sums
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Ring_sums/R.var" "Ring_sums__".
(*#*
*** Infinite Ring sums
*)
(* UNEXPORTED
-Section infinite_ring_sums.
+Section infinite_ring_sums
*)
inline "cic:/CoRN/algebra/CRings/Sum_upto.con".
inline "cic:/CoRN/algebra/CRings/Sum_from_upto_alt.con".
(* UNEXPORTED
-End infinite_ring_sums.
+End infinite_ring_sums
*)
(* UNEXPORTED
-Section ring_sums_over_lists.
+Section ring_sums_over_lists
*)
(*#* *** Ring Sums over Lists
inline "cic:/CoRN/algebra/CRings/List_Sum_from_upto.con".
(* UNEXPORTED
-End ring_sums_over_lists.
+End ring_sums_over_lists
*)
(* UNEXPORTED
-End Ring_sums.
+End Ring_sums
*)
(*#*
*)
(* UNEXPORTED
-Section Dist_properties.
+Section Dist_properties
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/Dist_properties/R.var" "Dist_properties__".
inline "cic:/CoRN/algebra/CRings/dist_1b.con".
inline "cic:/CoRN/algebra/CRings/sumx_const.con".
(* UNEXPORTED
-End Dist_properties.
+End Dist_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section NExp_properties.
+Section NExp_properties
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/NExp_properties/R.var" "NExp_properties__".
inline "cic:/CoRN/algebra/CRings/nexp_wd.con".
*)
(* UNEXPORTED
-End NExp_properties.
+End NExp_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CRing_Ops.
+Section CRing_Ops
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/R.var" "CRing_Ops__".
-inline "cic:/CoRN/algebra/CRings/F.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/F.var" "CRing_Ops__".
-inline "cic:/CoRN/algebra/CRings/G.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/G.var" "CRing_Ops__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CRings/P.con".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/P.con" "CRing_Ops__".
-inline "cic:/CoRN/algebra/CRings/Q.con".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/Q.con" "CRing_Ops__".
(* end hide *)
(* UNEXPORTED
-Section Part_Function_Mult.
+Section Part_Function_Mult
*)
inline "cic:/CoRN/algebra/CRings/part_function_mult_strext.con".
inline "cic:/CoRN/algebra/CRings/Fmult.con".
(* UNEXPORTED
-End Part_Function_Mult.
+End Part_Function_Mult
*)
(* UNEXPORTED
-Section Part_Function_Nth_Power.
+Section Part_Function_Nth_Power
*)
-inline "cic:/CoRN/algebra/CRings/n.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/Part_Function_Nth_Power/n.var" "CRing_Ops__Part_Function_Nth_Power__".
inline "cic:/CoRN/algebra/CRings/part_function_nth_strext.con".
inline "cic:/CoRN/algebra/CRings/Fnth.con".
(* UNEXPORTED
-End Part_Function_Nth_Power.
+End Part_Function_Nth_Power
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CRings/R'.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/R'.var" "CRing_Ops__".
inline "cic:/CoRN/algebra/CRings/included_FMult.con".
inline "cic:/CoRN/algebra/CRings/included_FMult''.con".
-inline "cic:/CoRN/algebra/CRings/n.var".
+inline "cic:/CoRN/algebra/CRings/CRing_Ops/n.var" "CRing_Ops__".
inline "cic:/CoRN/algebra/CRings/included_FNth.con".
inline "cic:/CoRN/algebra/CRings/included_FNth'.con".
(* UNEXPORTED
-End CRing_Ops.
+End CRing_Ops
*)
inline "cic:/CoRN/algebra/CRings/Fscalmult.con".
*)
(* UNEXPORTED
-Section ScalarMultiplication.
+Section ScalarMultiplication
*)
-inline "cic:/CoRN/algebra/CRings/R.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R.var" "ScalarMultiplication__".
-inline "cic:/CoRN/algebra/CRings/F.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/F.var" "ScalarMultiplication__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CRings/P.con".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/P.con" "ScalarMultiplication__".
(* end hide *)
-inline "cic:/CoRN/algebra/CRings/R'.var".
+inline "cic:/CoRN/algebra/CRings/ScalarMultiplication/R'.var" "ScalarMultiplication__".
inline "cic:/CoRN/algebra/CRings/included_FScalMult.con".
inline "cic:/CoRN/algebra/CRings/included_FScalMult'.con".
(* UNEXPORTED
-End ScalarMultiplication.
+End ScalarMultiplication
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CSemiGroup_axioms.
+Section CSemiGroup_axioms
*)
-inline "cic:/CoRN/algebra/CSemiGroups/G.var".
+inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_axioms/G.var" "CSemiGroup_axioms__".
inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_is_CSemiGroup.con".
inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc.con".
(* UNEXPORTED
-End CSemiGroup_axioms.
+End CSemiGroup_axioms
*)
(* Begin_SpecReals *)
*)
(* UNEXPORTED
-Section CSemiGroup_basics.
+Section CSemiGroup_basics
*)
-inline "cic:/CoRN/algebra/CSemiGroups/G.var".
+inline "cic:/CoRN/algebra/CSemiGroups/CSemiGroup_basics/G.var" "CSemiGroup_basics__".
(* End_SpecReals *)
inline "cic:/CoRN/algebra/CSemiGroups/plus_assoc_unfolded.con".
(* UNEXPORTED
-End CSemiGroup_basics.
+End CSemiGroup_basics
*)
(* End_SpecReals *)
*)
(* UNEXPORTED
-Section Part_Function_Plus.
+Section Part_Function_Plus
*)
-inline "cic:/CoRN/algebra/CSemiGroups/G.var".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/G.var" "Part_Function_Plus__".
-inline "cic:/CoRN/algebra/CSemiGroups/F.var".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F.var" "Part_Function_Plus__".
-inline "cic:/CoRN/algebra/CSemiGroups/F'.var".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/F'.var" "Part_Function_Plus__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CSemiGroups/P.con".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/P.con" "Part_Function_Plus__".
-inline "cic:/CoRN/algebra/CSemiGroups/Q.con".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/Q.con" "Part_Function_Plus__".
(* end hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CSemiGroups/R.var".
+inline "cic:/CoRN/algebra/CSemiGroups/Part_Function_Plus/R.var" "Part_Function_Plus__".
inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus.con".
inline "cic:/CoRN/algebra/CSemiGroups/included_FPlus''.con".
(* UNEXPORTED
-End Part_Function_Plus.
+End Part_Function_Plus
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section SubCSemiGroups.
+Section SubCSemiGroups
*)
-inline "cic:/CoRN/algebra/CSemiGroups/csg.var".
+inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/csg.var" "SubCSemiGroups__".
-inline "cic:/CoRN/algebra/CSemiGroups/P.var".
+inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/P.var" "SubCSemiGroups__".
-inline "cic:/CoRN/algebra/CSemiGroups/op_pres_P.var".
+inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/op_pres_P.var" "SubCSemiGroups__".
-inline "cic:/CoRN/algebra/CSemiGroups/subcrr.con".
+inline "cic:/CoRN/algebra/CSemiGroups/SubCSemiGroups/subcrr.con" "SubCSemiGroups__".
inline "cic:/CoRN/algebra/CSemiGroups/Build_SubCSemiGroup.con".
(* UNEXPORTED
-End SubCSemiGroups.
+End SubCSemiGroups
*)
include "algebra/CSetoids.ma".
(* UNEXPORTED
-Section unary_function_composition.
+Section unary_function_composition
*)
(*#* ** Composition of Setoid functions
setoid function from [S1] to [S2], and [g] from [S2]
to [S3] in the following definition of composition. *)
-inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
+inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S1.var" "unary_function_composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
+inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S2.var" "unary_function_composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
+inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/S3.var" "unary_function_composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/f.var".
+inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/f.var" "unary_function_composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/g.var".
+inline "cic:/CoRN/algebra/CSetoidFun/unary_function_composition/g.var" "unary_function_composition__".
inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_fun.con".
(* UNEXPORTED
-End unary_function_composition.
+End unary_function_composition
*)
(* UNEXPORTED
-Section unary_and_binary_function_composition.
+Section unary_and_binary_function_composition
*)
inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_bin_un_fun.con".
inline "cic:/CoRN/algebra/CSetoidFun/compose_CSetoid_un_bin_fun.con".
(* UNEXPORTED
-End unary_and_binary_function_composition.
+End unary_and_binary_function_composition
*)
(*#* ***Projections
*)
(* UNEXPORTED
-Section function_projection.
+Section function_projection
*)
inline "cic:/CoRN/algebra/CSetoidFun/proj_bin_fun.con".
inline "cic:/CoRN/algebra/CSetoidFun/projected_bin_fun.con".
(* UNEXPORTED
-End function_projection.
+End function_projection
*)
(* UNEXPORTED
-Section BinProj.
+Section BinProj
*)
-inline "cic:/CoRN/algebra/CSetoidFun/S.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinProj/S.var" "BinProj__".
inline "cic:/CoRN/algebra/CSetoidFun/binproj1.con".
inline "cic:/CoRN/algebra/CSetoidFun/cs_binproj1.con".
(* UNEXPORTED
-End BinProj.
+End BinProj
*)
(*#* **Combining operations
*)
(* UNEXPORTED
-Section CombiningOperations.
+Section CombiningOperations
*)
-inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S1.var" "CombiningOperations__".
-inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S2.var" "CombiningOperations__".
-inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/S3.var" "CombiningOperations__".
(*#*
In the following definition, we assume [f] is a setoid function from
*)
(* UNEXPORTED
-Section CombiningUnaryOperations.
+Section CombiningUnaryOperations
*)
-inline "cic:/CoRN/algebra/CSetoidFun/f.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/f.var" "CombiningOperations__CombiningUnaryOperations__".
-inline "cic:/CoRN/algebra/CSetoidFun/op.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CombiningOperations/CombiningUnaryOperations/op.var" "CombiningOperations__CombiningUnaryOperations__".
inline "cic:/CoRN/algebra/CSetoidFun/opOnFun.con".
(* UNEXPORTED
-End CombiningUnaryOperations.
+End CombiningUnaryOperations
*)
(* UNEXPORTED
-End CombiningOperations.
+End CombiningOperations
*)
(*#* **Partial Functions
*)
(* UNEXPORTED
-Section SubSets_of_G.
+Section SubSets_of_G
*)
(*#* ***Subsets of Setoids
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CSetoidFun/S.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/S.var" "SubSets_of_G__".
(* UNEXPORTED
-Section Conjunction.
+Section Conjunction
*)
-inline "cic:/CoRN/algebra/CSetoidFun/P.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/P.var" "SubSets_of_G__Conjunction__".
-inline "cic:/CoRN/algebra/CSetoidFun/Q.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Conjunction/Q.var" "SubSets_of_G__Conjunction__".
inline "cic:/CoRN/algebra/CSetoidFun/conjP.con".
inline "cic:/CoRN/algebra/CSetoidFun/conj_wd.con".
(* UNEXPORTED
-End Conjunction.
+End Conjunction
*)
(* UNEXPORTED
-Section Disjunction.
+Section Disjunction
*)
-inline "cic:/CoRN/algebra/CSetoidFun/P.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/P.var" "SubSets_of_G__Disjunction__".
-inline "cic:/CoRN/algebra/CSetoidFun/Q.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Disjunction/Q.var" "SubSets_of_G__Disjunction__".
(*#*
Although at this stage we never use it, for completeness's sake we also treat disjunction (corresponding to union of subsets).
inline "cic:/CoRN/algebra/CSetoidFun/disj_wd.con".
(* UNEXPORTED
-End Disjunction.
+End Disjunction
*)
(* UNEXPORTED
-Section Extension.
+Section Extension
*)
(*#*
The next definition is a bit tricky, and is useful for choosing among the elements that satisfy a predicate [P] those that also satisfy [R] in the case where [R] is only defined for elements satisfying [P]---consider [R] to be a condition on the image of an object via a function with domain [P]. We chose to call this operation [extension].
*)
-inline "cic:/CoRN/algebra/CSetoidFun/P.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/P.var" "SubSets_of_G__Extension__".
-inline "cic:/CoRN/algebra/CSetoidFun/R.var".
+inline "cic:/CoRN/algebra/CSetoidFun/SubSets_of_G/Extension/R.var" "SubSets_of_G__Extension__".
inline "cic:/CoRN/algebra/CSetoidFun/extend.con".
inline "cic:/CoRN/algebra/CSetoidFun/extension_wd.con".
(* UNEXPORTED
-End Extension.
+End Extension
*)
(* UNEXPORTED
-End SubSets_of_G.
+End SubSets_of_G
*)
(* NOTATION
*)
(* UNEXPORTED
-Section CSetoid_Ops.
+Section CSetoid_Ops
*)
-inline "cic:/CoRN/algebra/CSetoidFun/S.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/S.var" "CSetoid_Ops__".
(*#*
To begin with, we want to be able to ``see'' each total function as a partial function.
inline "cic:/CoRN/algebra/CSetoidFun/total_eq_part.con".
(* UNEXPORTED
-Section Part_Function_Const.
+Section Part_Function_Const
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CSetoidFun/c.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Const/c.var" "CSetoid_Ops__Part_Function_Const__".
inline "cic:/CoRN/algebra/CSetoidFun/Fconst.con".
(* UNEXPORTED
-End Part_Function_Const.
+End Part_Function_Const
*)
(* UNEXPORTED
-Section Part_Function_Id.
+Section Part_Function_Id
*)
inline "cic:/CoRN/algebra/CSetoidFun/Fid.con".
(* UNEXPORTED
-End Part_Function_Id.
+End Part_Function_Id
*)
(*#*
*)
(* UNEXPORTED
-Section Part_Function_Composition.
+Section Part_Function_Composition
*)
-inline "cic:/CoRN/algebra/CSetoidFun/G.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/G.var" "CSetoid_Ops__Part_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/F.var".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/F.var" "CSetoid_Ops__Part_Function_Composition__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CSetoidFun/P.con".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/P.con" "CSetoid_Ops__Part_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/Q.con".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/Q.con" "CSetoid_Ops__Part_Function_Composition__".
(* end hide *)
-inline "cic:/CoRN/algebra/CSetoidFun/R.con".
+inline "cic:/CoRN/algebra/CSetoidFun/CSetoid_Ops/Part_Function_Composition/R.con" "CSetoid_Ops__Part_Function_Composition__".
inline "cic:/CoRN/algebra/CSetoidFun/part_function_comp_strext.con".
inline "cic:/CoRN/algebra/CSetoidFun/Fcomp.con".
(* UNEXPORTED
-End Part_Function_Composition.
+End Part_Function_Composition
*)
(* UNEXPORTED
-End CSetoid_Ops.
+End CSetoid_Ops
*)
(*#*
*)
(* UNEXPORTED
-Section BinPart_Function_Composition.
+Section BinPart_Function_Composition
*)
-inline "cic:/CoRN/algebra/CSetoidFun/S1.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S1.var" "BinPart_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/S2.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S2.var" "BinPart_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/S3.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/S3.var" "BinPart_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/G.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/G.var" "BinPart_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/F.var".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/F.var" "BinPart_Function_Composition__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CSetoidFun/P.con".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/P.con" "BinPart_Function_Composition__".
-inline "cic:/CoRN/algebra/CSetoidFun/Q.con".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/Q.con" "BinPart_Function_Composition__".
(* end hide *)
-inline "cic:/CoRN/algebra/CSetoidFun/R.con".
+inline "cic:/CoRN/algebra/CSetoidFun/BinPart_Function_Composition/R.con" "BinPart_Function_Composition__".
inline "cic:/CoRN/algebra/CSetoidFun/bin_part_function_comp_strext.con".
inline "cic:/CoRN/algebra/CSetoidFun/BinFcomp.con".
(* UNEXPORTED
-End BinPart_Function_Composition.
+End BinPart_Function_Composition
*)
(* Different tokens for compatibility with coqdoc *)
*)
(* UNEXPORTED
-Section bijections.
+Section bijections
*)
(*#* **Bijections *)
inline "cic:/CoRN/algebra/CSetoidFun/Inv_bij.con".
(* UNEXPORTED
-End bijections.
+End bijections
*)
(* UNEXPORTED
include "algebra/CSetoidFun.ma".
(* UNEXPORTED
-Section inclusion.
+Section inclusion
*)
(*#* ** Inclusion
Let [S] be a setoid, and [P], [Q], [R] be predicates on [S]. *)
-inline "cic:/CoRN/algebra/CSetoidInc/S.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/S.var" "inclusion__".
inline "cic:/CoRN/algebra/CSetoidInc/included.con".
(* UNEXPORTED
-Section Basics.
+Section Basics
*)
-inline "cic:/CoRN/algebra/CSetoidInc/P.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/P.var" "inclusion__Basics__".
-inline "cic:/CoRN/algebra/CSetoidInc/Q.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/Q.var" "inclusion__Basics__".
-inline "cic:/CoRN/algebra/CSetoidInc/R.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Basics/R.var" "inclusion__Basics__".
inline "cic:/CoRN/algebra/CSetoidInc/included_refl.con".
inline "cic:/CoRN/algebra/CSetoidInc/included_extend.con".
(* UNEXPORTED
-End Basics.
+End Basics
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CSetoidInc/F.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/F.var" "inclusion__".
-inline "cic:/CoRN/algebra/CSetoidInc/G.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/G.var" "inclusion__".
(* begin hide *)
-inline "cic:/CoRN/algebra/CSetoidInc/P.con".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/P.con" "inclusion__".
-inline "cic:/CoRN/algebra/CSetoidInc/Q.con".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/Q.con" "inclusion__".
(* end hide *)
-inline "cic:/CoRN/algebra/CSetoidInc/R.var".
+inline "cic:/CoRN/algebra/CSetoidInc/inclusion/R.var" "inclusion__".
inline "cic:/CoRN/algebra/CSetoidInc/included_FComp.con".
inline "cic:/CoRN/algebra/CSetoidInc/included_FComp'.con".
(* UNEXPORTED
-End inclusion.
+End inclusion
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Properties_of_relations.
+Section Properties_of_relations
*)
-inline "cic:/CoRN/algebra/CSetoids/A.var".
+inline "cic:/CoRN/algebra/CSetoids/Properties_of_relations/A.var" "Properties_of_relations__".
inline "cic:/CoRN/algebra/CSetoids/irreflexive.con".
inline "cic:/CoRN/algebra/CSetoids/antisymmetric.con".
(* UNEXPORTED
-End Properties_of_relations.
+End Properties_of_relations
*)
(* begin hide *)
(* Begin_SpecReals *)
(* UNEXPORTED
-Section CSetoid_axioms.
+Section CSetoid_axioms
*)
-inline "cic:/CoRN/algebra/CSetoids/S.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_axioms/S.var" "CSetoid_axioms__".
inline "cic:/CoRN/algebra/CSetoids/CSetoid_is_CSetoid.con".
inline "cic:/CoRN/algebra/CSetoids/ap_tight.con".
(* UNEXPORTED
-End CSetoid_axioms.
+End CSetoid_axioms
*)
(* End_SpecReals *)
(* Begin_SpecReals *)
(* UNEXPORTED
-Section CSetoid_basics.
+Section CSetoid_basics
*)
-inline "cic:/CoRN/algebra/CSetoids/S.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_basics/S.var" "CSetoid_basics__".
(* End_SpecReals *)
(* Begin_SpecReals *)
(* UNEXPORTED
-End CSetoid_basics.
+End CSetoid_basics
*)
(* End_SpecReals *)
(* UNEXPORTED
-Section product_csetoid.
+Section product_csetoid
*)
(*#* **The product of setoids *)
inline "cic:/CoRN/algebra/CSetoids/ProdCSetoid.con".
(* UNEXPORTED
-End product_csetoid.
+End product_csetoid
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CSetoid_relations_and_predicates.
+Section CSetoid_relations_and_predicates
*)
-inline "cic:/CoRN/algebra/CSetoids/S.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/S.var" "CSetoid_relations_and_predicates__".
(* End_SpecReals *)
*)
(* UNEXPORTED
-Section CSetoidPredicates.
+Section CSetoidPredicates
*)
-inline "cic:/CoRN/algebra/CSetoids/P.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPredicates/P.var" "CSetoid_relations_and_predicates__CSetoidPredicates__".
inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext.con".
inline "cic:/CoRN/algebra/CSetoids/pred_wd.con".
(* UNEXPORTED
-End CSetoidPredicates.
+End CSetoidPredicates
*)
inline "cic:/CoRN/algebra/CSetoids/CSetoid_predicate.ind".
(*#* Similar, with [Prop] instead of [CProp]. *)
(* UNEXPORTED
-Section CSetoidPPredicates.
+Section CSetoidPPredicates
*)
-inline "cic:/CoRN/algebra/CSetoids/P.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CSetoidPPredicates/P.var" "CSetoid_relations_and_predicates__CSetoidPPredicates__".
inline "cic:/CoRN/algebra/CSetoids/pred_strong_ext'.con".
inline "cic:/CoRN/algebra/CSetoids/pred_wd'.con".
(* UNEXPORTED
-End CSetoidPPredicates.
+End CSetoidPPredicates
*)
(*#* ***Definition of a setoid predicate *)
%\end{convention}% *)
(* UNEXPORTED
-Section CsetoidRelations.
+Section CsetoidRelations
*)
-inline "cic:/CoRN/algebra/CSetoids/R.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CsetoidRelations/R.var" "CSetoid_relations_and_predicates__CsetoidRelations__".
inline "cic:/CoRN/algebra/CSetoids/rel_wdr.con".
(* Begin_SpecReals *)
(* UNEXPORTED
-End CsetoidRelations.
+End CsetoidRelations
*)
(*#* ***Definition of a setoid relation
*)
(* UNEXPORTED
-Section CCsetoidRelations.
+Section CCsetoidRelations
*)
-inline "cic:/CoRN/algebra/CSetoids/R.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_relations_and_predicates/CCsetoidRelations/R.var" "CSetoid_relations_and_predicates__CCsetoidRelations__".
inline "cic:/CoRN/algebra/CSetoids/Crel_wdr.con".
(* Begin_SpecReals *)
(* UNEXPORTED
-End CCsetoidRelations.
+End CCsetoidRelations
*)
(*#* ***Definition of a [CProp] setoid relation
(* Begin_SpecReals *)
(* UNEXPORTED
-End CSetoid_relations_and_predicates.
+End CSetoid_relations_and_predicates
*)
(* UNEXPORTED
(* Begin_SpecReals *)
(* UNEXPORTED
-Section CSetoid_functions.
+Section CSetoid_functions
*)
-inline "cic:/CoRN/algebra/CSetoids/S1.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S1.var" "CSetoid_functions__".
-inline "cic:/CoRN/algebra/CSetoids/S2.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S2.var" "CSetoid_functions__".
-inline "cic:/CoRN/algebra/CSetoids/S3.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/S3.var" "CSetoid_functions__".
(* UNEXPORTED
-Section unary_functions.
+Section unary_functions
*)
(*#*
[f] is a function from (the carrier of) [S1] to
(the carrier of) [S2]. *)
-inline "cic:/CoRN/algebra/CSetoids/f.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/unary_functions/f.var" "CSetoid_functions__unary_functions__".
inline "cic:/CoRN/algebra/CSetoids/fun_wd.con".
(* Begin_SpecReals *)
(* UNEXPORTED
-End unary_functions.
+End unary_functions
*)
inline "cic:/CoRN/algebra/CSetoids/CSetoid_fun.ind".
(* Begin_SpecReals *)
(* UNEXPORTED
-Section binary_functions.
+Section binary_functions
*)
(*#*
[f] is a function from [S1] and [S2] to [S3].
*)
-inline "cic:/CoRN/algebra/CSetoids/f.var".
+inline "cic:/CoRN/algebra/CSetoids/CSetoid_functions/binary_functions/f.var" "CSetoid_functions__binary_functions__".
inline "cic:/CoRN/algebra/CSetoids/bin_fun_wd.con".
(* Begin_SpecReals *)
(* UNEXPORTED
-End binary_functions.
+End binary_functions
*)
inline "cic:/CoRN/algebra/CSetoids/CSetoid_bin_fun.ind".
inline "cic:/CoRN/algebra/CSetoids/csbf_wd_unfolded.con".
(* UNEXPORTED
-End CSetoid_functions.
+End CSetoid_functions
*)
(* End_SpecReals *)
*)
(* UNEXPORTED
-Section csetoid_inner_ops.
+Section csetoid_inner_ops
*)
-inline "cic:/CoRN/algebra/CSetoids/S.var".
+inline "cic:/CoRN/algebra/CSetoids/csetoid_inner_ops/S.var" "csetoid_inner_ops__".
(*#* Properties of binary operations *)
(* Begin_SpecReals *)
(* UNEXPORTED
-End csetoid_inner_ops.
+End csetoid_inner_ops
*)
(* End_SpecReals *)
*)
(* UNEXPORTED
-Section csetoid_outer_ops.
+Section csetoid_outer_ops
*)
-inline "cic:/CoRN/algebra/CSetoids/S1.var".
+inline "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S1.var" "csetoid_outer_ops__".
-inline "cic:/CoRN/algebra/CSetoids/S2.var".
+inline "cic:/CoRN/algebra/CSetoids/csetoid_outer_ops/S2.var" "csetoid_outer_ops__".
(*#*
Well-defined outer operations on a setoid.
inline "cic:/CoRN/algebra/CSetoids/csoo_wd_unfolded.con".
(* UNEXPORTED
-End csetoid_outer_ops.
+End csetoid_outer_ops
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section SubCSetoids.
+Section SubCSetoids
*)
-inline "cic:/CoRN/algebra/CSetoids/S.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/S.var" "SubCSetoids__".
-inline "cic:/CoRN/algebra/CSetoids/P.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/P.var" "SubCSetoids__".
inline "cic:/CoRN/algebra/CSetoids/subcsetoid_crr.ind".
*)
(* UNEXPORTED
-Section SubCSetoid_unary_operations.
+Section SubCSetoid_unary_operations
*)
-inline "cic:/CoRN/algebra/CSetoids/f.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/f.var" "SubCSetoids__SubCSetoid_unary_operations__".
inline "cic:/CoRN/algebra/CSetoids/un_op_pres_pred.con".
Assume [pr:un_op_pres_pred].
%\end{convention}% *)
-inline "cic:/CoRN/algebra/CSetoids/pr.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_unary_operations/pr.var" "SubCSetoids__SubCSetoid_unary_operations__".
inline "cic:/CoRN/algebra/CSetoids/restr_un_op.con".
inline "cic:/CoRN/algebra/CSetoids/Build_SubCSetoid_un_op.con".
(* UNEXPORTED
-End SubCSetoid_unary_operations.
+End SubCSetoid_unary_operations
*)
(*#* ***Subsetoid binary operations
*)
(* UNEXPORTED
-Section SubCSetoid_binary_operations.
+Section SubCSetoid_binary_operations
*)
-inline "cic:/CoRN/algebra/CSetoids/f.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/f.var" "SubCSetoids__SubCSetoid_binary_operations__".
inline "cic:/CoRN/algebra/CSetoids/bin_op_pres_pred.con".
%\end{convention}%
*)
-inline "cic:/CoRN/algebra/CSetoids/pr.var".
+inline "cic:/CoRN/algebra/CSetoids/SubCSetoids/SubCSetoid_binary_operations/pr.var" "SubCSetoids__SubCSetoid_binary_operations__".
inline "cic:/CoRN/algebra/CSetoids/restr_bin_op.con".
inline "cic:/CoRN/algebra/CSetoids/restr_f_assoc.con".
(* UNEXPORTED
-End SubCSetoid_binary_operations.
+End SubCSetoid_binary_operations
*)
(* Begin_SpecReals *)
(* UNEXPORTED
-End SubCSetoids.
+End SubCSetoids
*)
(* End_SpecReals *)
*)
(* UNEXPORTED
-Section Sums.
+Section Sums
*)
-inline "cic:/CoRN/algebra/CSums/G.var".
+inline "cic:/CoRN/algebra/CSums/Sums/G.var" "Sums__".
(* Sum1 and Sum use subtraction *)
inline "cic:/CoRN/algebra/CSums/Sumx_Sum0.con".
(* UNEXPORTED
-End Sums.
+End Sums
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Sums.
+Section More_Sums
*)
-inline "cic:/CoRN/algebra/CSums/G.var".
+inline "cic:/CoRN/algebra/CSums/More_Sums/G.var" "More_Sums__".
inline "cic:/CoRN/algebra/CSums/Mengolli_Sum.con".
inline "cic:/CoRN/algebra/CSums/Sumx_to_Sum.con".
(* UNEXPORTED
-End More_Sums.
+End More_Sums
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section VS_basics.
+Section VS_basics
*)
-inline "cic:/CoRN/algebra/CVectorSpace/F.var".
+inline "cic:/CoRN/algebra/CVectorSpace/VS_basics/F.var" "VS_basics__".
-inline "cic:/CoRN/algebra/CVectorSpace/V.var".
+inline "cic:/CoRN/algebra/CVectorSpace/VS_basics/V.var" "VS_basics__".
inline "cic:/CoRN/algebra/CVectorSpace/vs_op_zero.con".
inline "cic:/CoRN/algebra/CVectorSpace/vs_op_resp_ap_lft.con".
(* UNEXPORTED
-End VS_basics.
+End VS_basics
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Structure.
+Section Structure
*)
-inline "cic:/CoRN/algebra/Cauchy_COF/F.var".
+inline "cic:/CoRN/algebra/Cauchy_COF/Structure/F.var" "Structure__".
(*#*
** Setoid Structure
inline "cic:/CoRN/algebra/Cauchy_COF/R_Set.con".
(* UNEXPORTED
-Section CSetoid_Structure.
+Section CSetoid_Structure
*)
inline "cic:/CoRN/algebra/Cauchy_COF/R_lt.con".
inline "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con".
(* UNEXPORTED
-End CSetoid_Structure.
+End CSetoid_Structure
*)
(* UNEXPORTED
-Section Group_Structure.
+Section Group_Structure
*)
(*#*
inline "cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con".
(* UNEXPORTED
-End Group_Structure.
+End Group_Structure
*)
(* UNEXPORTED
-Section Ring_Structure.
+Section Ring_Structure
*)
(*#* ** Ring Structure
inline "cic:/CoRN/algebra/Cauchy_COF/R_CRing.con".
(* UNEXPORTED
-End Ring_Structure.
+End Ring_Structure
*)
(* UNEXPORTED
-Section Field_Structure.
+Section Field_Structure
*)
(*#* ** Field Structure
inline "cic:/CoRN/algebra/Cauchy_COF/R_CField.con".
(* UNEXPORTED
-End Field_Structure.
+End Field_Structure
*)
(* UNEXPORTED
-Section Order.
+Section Order
*)
(*#* ** Order Structure
inline "cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con".
(* UNEXPORTED
-End Order.
+End Order
*)
(*#*
*)
(* UNEXPORTED
-Section Auxiliary.
+Section Auxiliary
*)
inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_1.con".
inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con".
(* UNEXPORTED
-End Auxiliary.
+End Auxiliary
*)
(* UNEXPORTED
-End Structure.
+End Structure
*)
*)
(* UNEXPORTED
-Section More_Nexp.
+Section More_Nexp
*)
-inline "cic:/CoRN/algebra/Expon/R.var".
+inline "cic:/CoRN/algebra/Expon/More_Nexp/R.var" "More_Nexp__".
inline "cic:/CoRN/algebra/Expon/nexp_resp_ap_zero.con".
inline "cic:/CoRN/algebra/Expon/bin_less_un.con".
(* UNEXPORTED
-End More_Nexp.
+End More_Nexp
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Zexp_def.
+Section Zexp_def
*)
-inline "cic:/CoRN/algebra/Expon/R.var".
+inline "cic:/CoRN/algebra/Expon/Zexp_def/R.var" "Zexp_def__".
(*#*
It would be nicer to define [zexp] using [caseZdiff], but we already
inline "cic:/CoRN/algebra/Expon/zexp.con".
(* UNEXPORTED
-End Zexp_def.
+End Zexp_def
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Zexp_properties.
+Section Zexp_properties
*)
-inline "cic:/CoRN/algebra/Expon/R.var".
+inline "cic:/CoRN/algebra/Expon/Zexp_properties/R.var" "Zexp_properties__".
inline "cic:/CoRN/algebra/Expon/zexp_zero.con".
inline "cic:/CoRN/algebra/Expon/zexp_pos.con".
(* UNEXPORTED
-End Zexp_properties.
+End Zexp_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Root_Unique.
+Section Root_Unique
*)
-inline "cic:/CoRN/algebra/Expon/R.var".
+inline "cic:/CoRN/algebra/Expon/Root_Unique/R.var" "Root_Unique__".
inline "cic:/CoRN/algebra/Expon/root_unique.con".
inline "cic:/CoRN/algebra/Expon/root_one.con".
(* UNEXPORTED
-End Root_Unique.
+End Root_Unique
*)
*)
(* UNEXPORTED
-Section List.
+Section List
*)
-inline "cic:/CoRN/algebra/ListType/A.var".
+inline "cic:/CoRN/algebra/ListType/List/A.var" "List__".
inline "cic:/CoRN/algebra/ListType/list.ind".
(*#*****************************)
(* UNEXPORTED
-Section length_order.
+Section length_order
*)
inline "cic:/CoRN/algebra/ListType/lel.con".
Hint Unfold lel: list.
*)
-inline "cic:/CoRN/algebra/ListType/a.var".
+inline "cic:/CoRN/algebra/ListType/List/length_order/a.var" "List__length_order__".
-inline "cic:/CoRN/algebra/ListType/b.var".
+inline "cic:/CoRN/algebra/ListType/List/length_order/b.var" "List__length_order__".
-inline "cic:/CoRN/algebra/ListType/l.var".
+inline "cic:/CoRN/algebra/ListType/List/length_order/l.var" "List__length_order__".
-inline "cic:/CoRN/algebra/ListType/m.var".
+inline "cic:/CoRN/algebra/ListType/List/length_order/m.var" "List__length_order__".
-inline "cic:/CoRN/algebra/ListType/n.var".
+inline "cic:/CoRN/algebra/ListType/List/length_order/n.var" "List__length_order__".
inline "cic:/CoRN/algebra/ListType/lel_refl.con".
inline "cic:/CoRN/algebra/ListType/lel_nil.con".
(* UNEXPORTED
-End length_order.
+End length_order
*)
(* UNEXPORTED
inline "cic:/CoRN/algebra/ListType/incl_app.con".
(* UNEXPORTED
-End List.
+End List
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Map.
+Section Map
*)
-inline "cic:/CoRN/algebra/ListType/A.var".
+inline "cic:/CoRN/algebra/ListType/Map/A.var" "Map__".
-inline "cic:/CoRN/algebra/ListType/B.var".
+inline "cic:/CoRN/algebra/ListType/Map/B.var" "Map__".
-inline "cic:/CoRN/algebra/ListType/f.var".
+inline "cic:/CoRN/algebra/ListType/Map/f.var" "Map__".
inline "cic:/CoRN/algebra/ListType/map.con".
(* UNEXPORTED
-End Map.
+End Map
*)
(* UNEXPORTED
** Properties of [AbsCC] *)
(* UNEXPORTED
-Section AbsCC_properties.
+Section AbsCC_properties
*)
inline "cic:/CoRN/complex/AbsCC/AbsCC_nonneg.con".
(* begin hide *)
-inline "cic:/CoRN/complex/AbsCC/l_1_1_2.con".
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_1_2.con" "AbsCC_properties__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/complex/AbsCC/l_1_2_3_CC.con".
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_1_2_3_CC.con" "AbsCC_properties__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/complex/AbsCC/l_4_1_2.con".
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_1_2.con" "AbsCC_properties__".
-inline "cic:/CoRN/complex/AbsCC/l_4_2_3.con".
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_2_3.con" "AbsCC_properties__".
-inline "cic:/CoRN/complex/AbsCC/l_4_3_4.con".
+inline "cic:/CoRN/complex/AbsCC/AbsCC_properties/l_4_3_4.con" "AbsCC_properties__".
(* end hide *)
(* UNEXPORTED
-End AbsCC_properties.
+End AbsCC_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Complex_Numbers.
+Section Complex_Numbers
*)
inline "cic:/CoRN/complex/CComplex/CC_set.ind".
inline "cic:/CoRN/complex/CComplex/TwoCC_ap_zero.con".
(* UNEXPORTED
-End Complex_Numbers.
+End Complex_Numbers
*)
(* begin hide *)
(*#* ** Properties of [II] *)
(* UNEXPORTED
-Section I_properties.
+Section I_properties
*)
inline "cic:/CoRN/complex/CComplex/I_square.con".
inline "cic:/CoRN/complex/CComplex/cc_calculate_square.con".
(* UNEXPORTED
-End I_properties.
+End I_properties
*)
(* UNEXPORTED
(*#* ** Properties of conjugation *)
(* UNEXPORTED
-Section Conj_properties.
+Section Conj_properties
*)
inline "cic:/CoRN/complex/CComplex/CC_conj_plus.con".
inline "cic:/CoRN/complex/CComplex/CC_conj_nexp.con".
(* UNEXPORTED
-End Conj_properties.
+End Conj_properties
*)
(* UNEXPORTED
(*#* ** Properties of the real axis *)
(* UNEXPORTED
-Section cc_IR_properties.
+Section cc_IR_properties
*)
inline "cic:/CoRN/complex/CComplex/Re_cc_IR.con".
inline "cic:/CoRN/complex/CComplex/cc_IR_nexp.con".
(* UNEXPORTED
-End cc_IR_properties.
+End cc_IR_properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section CC_ap_zero.
+Section CC_ap_zero
*)
inline "cic:/CoRN/complex/NRootCC/cc_ap_zero.con".
inline "cic:/CoRN/complex/NRootCC/C_cc_ap_zero.con".
(* UNEXPORTED
-End CC_ap_zero.
+End CC_ap_zero
*)
(*#* Weird lemma. *)
(* UNEXPORTED
-Section Imag_to_Real.
+Section Imag_to_Real
*)
inline "cic:/CoRN/complex/NRootCC/imag_to_real.con".
(* UNEXPORTED
-End Imag_to_Real.
+End Imag_to_Real
*)
(*#* ** Roots of the imaginary unit *)
(* UNEXPORTED
-Section NRootI.
+Section NRootI
*)
inline "cic:/CoRN/complex/NRootCC/sqrt_Half.con".
inline "cic:/CoRN/complex/NRootCC/nroot_minus_I_nexp.con".
(* UNEXPORTED
-End NRootI.
+End NRootI
*)
(*#* ** Roots of complex numbers *)
(* UNEXPORTED
-Section NRootCC_1.
+Section NRootCC_1
*)
(*#* We define the nth root of a complex number with a non zero imaginary part.
*)
(* UNEXPORTED
-Section NRootCC_1_ap_real.
+Section NRootCC_1_ap_real
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/a.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a.var" "NRootCC_1__NRootCC_1_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/b.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b.var" "NRootCC_1__NRootCC_1_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/b_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b_.var" "NRootCC_1__NRootCC_1_ap_real__".
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/c2.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c2.con" "NRootCC_1__NRootCC_1_ap_real__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/c.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/c.con" "NRootCC_1__NRootCC_1_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/a'2.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'2.con" "NRootCC_1__NRootCC_1_ap_real__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/a'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/a'.con" "NRootCC_1__NRootCC_1_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/b'2.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'2.con" "NRootCC_1__NRootCC_1_ap_real__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/b'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_real/b'.con" "NRootCC_1__NRootCC_1_ap_real__".
(* end hide *)
inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_real.con".
(* UNEXPORTED
-End NRootCC_1_ap_real.
+End NRootCC_1_ap_real
*)
(*#* We now define the nth root of a complex number with a non zero real part.
*)
(* UNEXPORTED
-Section NRootCC_1_ap_imag.
+Section NRootCC_1_ap_imag
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/a.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a.var" "NRootCC_1__NRootCC_1_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/b.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b.var" "NRootCC_1__NRootCC_1_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/a_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a_.var" "NRootCC_1__NRootCC_1_ap_imag__".
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/c'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/c'.con" "NRootCC_1__NRootCC_1_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/a'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/a'.con" "NRootCC_1__NRootCC_1_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/b'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_1/NRootCC_1_ap_imag/b'.con" "NRootCC_1__NRootCC_1_ap_imag__".
(* end hide *)
inline "cic:/CoRN/complex/NRootCC/nrootCC_1_ap_imag.con".
(* UNEXPORTED
-End NRootCC_1_ap_imag.
+End NRootCC_1_ap_imag
*)
(*#* We now define the roots of arbitrary non zero complex numbers. *)
inline "cic:/CoRN/complex/NRootCC/nrootCC_1.con".
(* UNEXPORTED
-End NRootCC_1.
+End NRootCC_1
*)
(* UNEXPORTED
-Section NRootCC_2.
+Section NRootCC_2
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/n.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_2/n.var" "NRootCC_2__".
-inline "cic:/CoRN/complex/NRootCC/c.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_2/c.var" "NRootCC_2__".
-inline "cic:/CoRN/complex/NRootCC/z.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_2/z.var" "NRootCC_2__".
-inline "cic:/CoRN/complex/NRootCC/c_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_2/c_.var" "NRootCC_2__".
inline "cic:/CoRN/complex/NRootCC/nrootCC_2'.con".
inline "cic:/CoRN/complex/NRootCC/nrootCC_2.con".
(* UNEXPORTED
-End NRootCC_2.
+End NRootCC_2
*)
(* UNEXPORTED
-Section NRootCC_3.
+Section NRootCC_3
*)
inline "cic:/CoRN/complex/NRootCC/Im_poly.con".
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/a.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3/a.var" "NRootCC_3__".
-inline "cic:/CoRN/complex/NRootCC/b.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3/b.var" "NRootCC_3__".
-inline "cic:/CoRN/complex/NRootCC/b_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3/b_.var" "NRootCC_3__".
-inline "cic:/CoRN/complex/NRootCC/n.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3/n.var" "NRootCC_3__".
inline "cic:/CoRN/complex/NRootCC/nrCC3_poly''.con".
inline "cic:/CoRN/complex/NRootCC/nrootCC_3_degree.con".
(* UNEXPORTED
-End NRootCC_3.
+End NRootCC_3
*)
(* UNEXPORTED
-Section NRootCC_3'.
+Section NRootCC_3'
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/c.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/c.var" "NRootCC_3'__".
-inline "cic:/CoRN/complex/NRootCC/n.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/n.var" "NRootCC_3'__".
-inline "cic:/CoRN/complex/NRootCC/n_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_3'/n_.var" "NRootCC_3'__".
inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_poly.con".
inline "cic:/CoRN/complex/NRootCC/nrootCC_3'_degree.con".
(* UNEXPORTED
-End NRootCC_3'.
+End NRootCC_3'
*)
(* UNEXPORTED
-Section NRootCC_4.
+Section NRootCC_4
*)
(* UNEXPORTED
-Section NRootCC_4_ap_real.
+Section NRootCC_4_ap_real
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/a.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/a.var" "NRootCC_4__NRootCC_4_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/b.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b.var" "NRootCC_4__NRootCC_4_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/b_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/b_.var" "NRootCC_4__NRootCC_4_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/n.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n.var" "NRootCC_4__NRootCC_4_ap_real__".
-inline "cic:/CoRN/complex/NRootCC/n_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/n_.var" "NRootCC_4__NRootCC_4_ap_real__".
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/c.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/c.con" "NRootCC_4__NRootCC_4_ap_real__".
(* end hide *)
(* UNEXPORTED
-Section NRootCC_4_solutions.
+Section NRootCC_4_solutions
*)
(* UNEXPORTED
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/r2'.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__".
-inline "cic:/CoRN/complex/NRootCC/c2.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/c2.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__".
-inline "cic:/CoRN/complex/NRootCC/r2'_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_solutions/r2'_.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_solutions__".
(* UNEXPORTED
Hint Resolve nrootCC_3': algebra.
inline "cic:/CoRN/complex/NRootCC/nrCC4_a1'.con".
(* UNEXPORTED
-End NRootCC_4_solutions.
+End NRootCC_4_solutions
*)
(* UNEXPORTED
-Section NRootCC_4_equations.
+Section NRootCC_4_equations
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/r.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
-inline "cic:/CoRN/complex/NRootCC/r_property.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/r_property.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
-inline "cic:/CoRN/complex/NRootCC/y2.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
-inline "cic:/CoRN/complex/NRootCC/y2_property.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y2_property.var" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
inline "cic:/CoRN/complex/NRootCC/nrCC4_a2.con".
inline "cic:/CoRN/complex/NRootCC/nrCC4_y.con".
-inline "cic:/CoRN/complex/NRootCC/y.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/y.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
inline "cic:/CoRN/complex/NRootCC/nrCC4_x.con".
-inline "cic:/CoRN/complex/NRootCC/x.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/x.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
inline "cic:/CoRN/complex/NRootCC/nrCC4_a5.con".
inline "cic:/CoRN/complex/NRootCC/nrCC4_z.con".
-inline "cic:/CoRN/complex/NRootCC/z.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_real/NRootCC_4_equations/z.con" "NRootCC_4__NRootCC_4_ap_real__NRootCC_4_equations__".
inline "cic:/CoRN/complex/NRootCC/nrCC4_a7.con".
inline "cic:/CoRN/complex/NRootCC/nrCC4_a9.con".
(* UNEXPORTED
-End NRootCC_4_equations.
+End NRootCC_4_equations
*)
inline "cic:/CoRN/complex/NRootCC/nrCC4_a10.con".
inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_real.con".
(* UNEXPORTED
-End NRootCC_4_ap_real.
+End NRootCC_4_ap_real
*)
(* UNEXPORTED
-Section NRootCC_4_ap_imag.
+Section NRootCC_4_ap_imag
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/a.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a.var" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/b.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b.var" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/a_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a_.var" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/n.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n.var" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/n_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/n_.var" "NRootCC_4__NRootCC_4_ap_imag__".
(* begin hide *)
-inline "cic:/CoRN/complex/NRootCC/c'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/c'.con" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/a'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/a'.con" "NRootCC_4__NRootCC_4_ap_imag__".
-inline "cic:/CoRN/complex/NRootCC/b'.con".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_4/NRootCC_4_ap_imag/b'.con" "NRootCC_4__NRootCC_4_ap_imag__".
(* end hide *)
inline "cic:/CoRN/complex/NRootCC/nrootCC_4_ap_imag.con".
(* UNEXPORTED
-End NRootCC_4_ap_imag.
+End NRootCC_4_ap_imag
*)
inline "cic:/CoRN/complex/NRootCC/nrootCC_4.con".
(* UNEXPORTED
-End NRootCC_4.
+End NRootCC_4
*)
(*#* Finally, the general definition of nth root. *)
(* UNEXPORTED
-Section NRootCC_5.
+Section NRootCC_5
*)
inline "cic:/CoRN/complex/NRootCC/nrCC_5a2.con".
%\end{convention}%
*)
-inline "cic:/CoRN/complex/NRootCC/c.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_5/c.var" "NRootCC_5__".
-inline "cic:/CoRN/complex/NRootCC/c_.var".
+inline "cic:/CoRN/complex/NRootCC/NRootCC_5/c_.var" "NRootCC_5__".
inline "cic:/CoRN/complex/NRootCC/nrCC_5a4.con".
inline "cic:/CoRN/complex/NRootCC/nrootCC_5.con".
(* UNEXPORTED
-End NRootCC_5.
+End NRootCC_5
*)
(*#* Final definition *)
inline "cic:/CoRN/devel/loeb/IDA/Ch6/on.con".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_3_ary.con" "__".
(* blz 65 Example 1 *)
(* blz 66 Examples 2 *)
(* UNEXPORTED
-Section p66E2.
+Section p66E2
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/X.var" "p66E2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/f.var" "p66E2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/g.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/g.var" "p66E2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/h.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2/h.var" "p66E2__".
(* Check comp_as_bin_op.*)
(* Check assoc_comp.*)
(* UNEXPORTED
-End p66E2.
+End p66E2
*)
(* blz 66 Example 2eblok 1 *)
(* blz 66 Example % 4 *)
(* UNEXPORTED
-Section p66E2b4.
+Section p66E2b4
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p66E2b4/A.var" "p66E2b4__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/Astar_as_CSemiGroup.con".
(* UNEXPORTED
-End p66E2b4.
+End p66E2b4
*)
(* Definition 5 *)
(* blz 67 Remark 2 *)
(* UNEXPORTED
-Section p67R2.
+Section p67R2
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/X.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p67R2/X.var" "p67R2__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_unit_FS_id.con".
(* UNEXPORTED
-End p67R2.
+End p67R2
*)
(* blz 67 Remark 3 *)
(* blz 68 Example blok1 1 *)
(* UNEXPORTED
-Section p68E1b1.
+Section p68E1b1
*)
inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.ind".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/two_element_CMonoids.con".
(* UNEXPORTED
-End p68E1b1.
+End p68E1b1
*)
(* blz 68 Example blok2 1 *)
include "algebra/CMonoids.ma".
(* UNEXPORTED
-Section D9S.
+Section D9S
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M1.var" "D9S__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9S/M2.var" "D9S__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/dprod.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CSemiGroup.con".
(* UNEXPORTED
-End D9S.
+End D9S
*)
(* UNEXPORTED
-Section D9M.
+Section D9M
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M1.var" "D9M__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/D9M/M2.var" "D9M__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1e2_is_rht_unit.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/direct_product_as_CMonoid.con".
(* UNEXPORTED
-End D9M.
+End D9M
*)
(* blz 69 Example *)
(* UNEXPORTED
-Section p69E1.
+Section p69E1
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/PM1M2.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/PM1M2.con" "p69E1__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/uu.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/uu.con" "p69E1__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/e1u.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p69E1/e1u.con" "p69E1__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/ex_69.con".
(* UNEXPORTED
-End p69E1.
+End p69E1
*)
(* Theorem 11 *)
(* UNEXPORTED
-Section Th11.
+Section Th11
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/M.var" "Th11__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/I.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/I.var" "Th11__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/C.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/C.var" "Th11__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/Cunit.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/Cunit.var" "Th11__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/op_pres_C.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th11/op_pres_C.var" "Th11__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/K.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/K_is_Monoid.con".
(* UNEXPORTED
-End Th11.
+End Th11
*)
(* Theorem 12 *)
(* UNEXPORTED
-Section Th12.
+Section Th12
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th12/A.var" "Th12__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/nil_is_rht_unit.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/free_monoid_as_CMonoid.con".
(* UNEXPORTED
-End Th12.
+End Th12
*)
(* blz 70 text *)
(* UNEXPORTED
-Section p70text.
+Section p70text
*)
include "devel/loeb/per/lst2fun.ma".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p70text/A.con" "p70text__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/ZerolessOne.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/pres_plus_to_word.con".
(* UNEXPORTED
-End p70text.
+End p70text
*)
(* Definition 13 *)
(* UNEXPORTED
-Section Th13.
+Section Th13
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M1.var" "Th13__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th13/M2.var" "Th13__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphism.con".
(* UNEXPORTED
-End Th13.
+End Th13
*)
(* blz 71 Example 1 *)
(* UNEXPORTED
-Section p71E1.
+Section p71E1
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/M.var" "p71E1__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/c.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/c.var" "p71E1__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/power_CMonoid_CSetoid.con".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/is_generated_by.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/is_generated_by.var" "p71E1__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E1/f.con" "p71E1__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/surjective_f.con".
(* UNEXPORTED
-End p71E1.
+End p71E1
*)
(* UNEXPORTED
-Section p71E1'.
+Section p71E1'
*)
inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1_is_generated_by_u.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_injective_f.con".
(* UNEXPORTED
-End p71E1'.
+End p71E1'
*)
(* Print to_word_bijective.*)
(* UNEXPORTED
-Section p71E2.
+Section p71E2
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/A.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/A.var" "p71E2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/L.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2/L.con" "p71E2__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_strext.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/L_is_morphism.con".
(* UNEXPORTED
-End p71E2.
+End p71E2
*)
(* blz 71 Remark 1 *)
(* UNEXPORTED
-Section p71R1.
+Section p71R1
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/S1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S1.var" "p71R1__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/S2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R1/S2.var" "p71R1__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/morphism_of_CSemiGroups.con".
(* UNEXPORTED
-End p71R1.
+End p71R1
*)
(* UNEXPORTED
-Section p71R2.
+Section p71R2
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71R2/M.var" "p71R2__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/automorphism.con".
(* UNEXPORTED
-End p71R2.
+End p71R2
*)
(* Theorem 14 *)
(* UNEXPORTED
-Section Th14.
+Section Th14
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M1.var" "Th14__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/M2.var" "Th14__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/f.var" "Th14__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/isof.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th14/isof.var" "Th14__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_imp_bij.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/iso_inv.con".
(* UNEXPORTED
-End Th14.
+End Th14
*)
(* blz 71 Examples 2eblok 1 *)
(* UNEXPORTED
-Section p71E2b1.
+Section p71E2b1
*)
inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/not_isomorphic_M1_M2.con".
(* UNEXPORTED
-End p71E2b1.
+End p71E2b1
*)
(* UNEXPORTED
-Section p71E2b2.
+Section p71E2b2
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M1.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M1.var" "p71E2b2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M2.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/M2.var" "p71E2b2__".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/f.con".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/p71E2b2/f.con" "p71E2b2__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/f_strext'.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/isomorphic_PM1M2_PM2M1.con".
(* UNEXPORTED
-End p71E2b2.
+End p71E2b2
*)
(* UNEXPORTED
-Section Th15.
+Section Th15
*)
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/M.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/M.var" "Th15__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/cm_Sum.con".
-inline "cic:/CoRN/devel/loeb/IDA/Ch6/D.var".
+inline "cic:/CoRN/devel/loeb/IDA/Ch6/Th15/D.var" "Th15__".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/member.con".
inline "cic:/CoRN/devel/loeb/IDA/Ch6/Dbrack_as_CMonoid.con".
(* UNEXPORTED
-End Th15.
+End Th15
*)
*)
(* UNEXPORTED
-Section Continuity_for_CC.
+Section Continuity_for_CC
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/CC_Props/f.var".
+inline "cic:/CoRN/fta/CC_Props/Continuity_for_CC/f.var" "Continuity_for_CC__".
(* (CSetoid_un_op CC). *)
inline "cic:/CoRN/fta/CC_Props/poly_pres_lim.con".
(* UNEXPORTED
-End Continuity_for_CC.
+End Continuity_for_CC
*)
inline "cic:/CoRN/fta/CC_Props/seq_yields_zero.con".
*)
(* UNEXPORTED
-Section Mult_CC_Continuous.
+Section Mult_CC_Continuous
*)
inline "cic:/CoRN/fta/CPoly_Contin1/mult_absCC.con".
inline "cic:/CoRN/fta/CPoly_Contin1/mult_CC_contin.con".
(* UNEXPORTED
-End Mult_CC_Continuous.
+End Mult_CC_Continuous
*)
(* UNEXPORTED
-Section CPoly_CC_Continuous.
+Section CPoly_CC_Continuous
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/CPoly_Contin1/g.var".
+inline "cic:/CoRN/fta/CPoly_Contin1/CPoly_CC_Continuous/g.var" "CPoly_CC_Continuous__".
inline "cic:/CoRN/fta/CPoly_Contin1/cpoly_CC_contin.con".
inline "cic:/CoRN/fta/CPoly_Contin1/contin_polyCC.con".
(* UNEXPORTED
-End CPoly_CC_Continuous.
+End CPoly_CC_Continuous
*)
*)
(* UNEXPORTED
-Section Monomials.
+Section Monomials
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/CPoly_Rev/R.var".
+inline "cic:/CoRN/fta/CPoly_Rev/Monomials/R.var" "Monomials__".
(* begin hide *)
-inline "cic:/CoRN/fta/CPoly_Rev/RX.con".
+inline "cic:/CoRN/fta/CPoly_Rev/Monomials/RX.con" "Monomials__".
(* end hide *)
inline "cic:/CoRN/fta/CPoly_Rev/monom_sum.con".
(* UNEXPORTED
-End Monomials.
+End Monomials
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Poly_Reverse.
+Section Poly_Reverse
*)
-inline "cic:/CoRN/fta/CPoly_Rev/R.var".
+inline "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/R.var" "Poly_Reverse__".
(* begin hide *)
-inline "cic:/CoRN/fta/CPoly_Rev/RX.con".
+inline "cic:/CoRN/fta/CPoly_Rev/Poly_Reverse/RX.con" "Poly_Reverse__".
(* end hide *)
inline "cic:/CoRN/fta/CPoly_Rev/Rev_mult.con".
(* UNEXPORTED
-End Poly_Reverse.
+End Poly_Reverse
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Poly_Shifted.
+Section Poly_Shifted
*)
inline "cic:/CoRN/fta/CPoly_Shift/Shift.con".
inline "cic:/CoRN/fta/CPoly_Shift/Shift_monic.con".
(* UNEXPORTED
-End Poly_Shifted.
+End Poly_Shifted
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section FTA_reg'.
+Section FTA_reg'
*)
-inline "cic:/CoRN/fta/FTA/f.var".
+inline "cic:/CoRN/fta/FTA/FTA_reg'/f.var" "FTA_reg'__".
-inline "cic:/CoRN/fta/FTA/n.var".
+inline "cic:/CoRN/fta/FTA/FTA_reg'/n.var" "FTA_reg'__".
-inline "cic:/CoRN/fta/FTA/f_degree.var".
+inline "cic:/CoRN/fta/FTA/FTA_reg'/f_degree.var" "FTA_reg'__".
inline "cic:/CoRN/fta/FTA/FTA_reg'.con".
(* UNEXPORTED
-End FTA_reg'.
+End FTA_reg'
*)
(*#*
*)
(* UNEXPORTED
-Section FTA_1.
+Section FTA_1
*)
-inline "cic:/CoRN/fta/FTA/f.var".
+inline "cic:/CoRN/fta/FTA/FTA_1/f.var" "FTA_1__".
-inline "cic:/CoRN/fta/FTA/n.var".
+inline "cic:/CoRN/fta/FTA/FTA_1/n.var" "FTA_1__".
-inline "cic:/CoRN/fta/FTA/f_degree.var".
+inline "cic:/CoRN/fta/FTA/FTA_1/f_degree.var" "FTA_1__".
-inline "cic:/CoRN/fta/FTA/c.var".
+inline "cic:/CoRN/fta/FTA/FTA_1/c.var" "FTA_1__".
-inline "cic:/CoRN/fta/FTA/f_c.var".
+inline "cic:/CoRN/fta/FTA/FTA_1/f_c.var" "FTA_1__".
inline "cic:/CoRN/fta/FTA/FTA_1a.con".
-inline "cic:/CoRN/fta/FTA/g.con".
+inline "cic:/CoRN/fta/FTA/FTA_1/g.con" "FTA_1__".
inline "cic:/CoRN/fta/FTA/FTA_1b.con".
inline "cic:/CoRN/fta/FTA/FTA_1'.con".
(* UNEXPORTED
-End FTA_1.
+End FTA_1
*)
(* UNEXPORTED
-Section Fund_Thm_Alg.
+Section Fund_Thm_Alg
*)
inline "cic:/CoRN/fta/FTA/FTA'.con".
inline "cic:/CoRN/fta/FTA/FTA_a_la_Henk.con".
(* UNEXPORTED
-End Fund_Thm_Alg.
+End Fund_Thm_Alg
*)
*)
(* UNEXPORTED
-Section Seq_Exists.
+Section Seq_Exists
*)
-inline "cic:/CoRN/fta/FTAreg/n.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/n.var" "Seq_Exists__".
-inline "cic:/CoRN/fta/FTAreg/lt0n.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/lt0n.var" "Seq_Exists__".
(*#*
%\begin{convention}% Let [qK] be a real between 0 and 1, with
*)
(* UNEXPORTED
-Section Kneser_Sequence.
+Section Kneser_Sequence
*)
-inline "cic:/CoRN/fta/FTAreg/qK.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qK.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/zltq.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/zltq.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/qlt1.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/qlt1.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/q_prop.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/q_prop.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/p.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/mp.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/mp.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/c0.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/c0.var" "Seq_Exists__Kneser_Sequence__".
-inline "cic:/CoRN/fta/FTAreg/p0ltc0.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_Exists/Kneser_Sequence/p0ltc0.var" "Seq_Exists__Kneser_Sequence__".
inline "cic:/CoRN/fta/FTAreg/Knes_tup.ind".
inline "cic:/CoRN/fta/FTAreg/sK_prop2.con".
(* UNEXPORTED
-End Kneser_Sequence.
+End Kneser_Sequence
*)
(* UNEXPORTED
-Section Seq_Exists_Main.
+Section Seq_Exists_Main
*)
(*#* **Main results
inline "cic:/CoRN/fta/FTAreg/seq_exists.con".
(* UNEXPORTED
-End Seq_Exists_Main.
+End Seq_Exists_Main
*)
(* UNEXPORTED
-End Seq_Exists.
+End Seq_Exists
*)
(* UNEXPORTED
-Section N_Exists.
+Section N_Exists
*)
-inline "cic:/CoRN/fta/FTAreg/n.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/n.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/lt0n.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/lt0n.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/q.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/q.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/zleq.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/zleq.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/qlt1.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/qlt1.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/c.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/c.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/zltc.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/zltc.var" "N_Exists__".
(* begin hide *)
-inline "cic:/CoRN/fta/FTAreg/q_.con".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/q_.con" "N_Exists__".
(* end hide *)
-inline "cic:/CoRN/fta/FTAreg/e.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/e.var" "N_Exists__".
-inline "cic:/CoRN/fta/FTAreg/zlte.var".
+inline "cic:/CoRN/fta/FTAreg/N_Exists/zlte.var" "N_Exists__".
inline "cic:/CoRN/fta/FTAreg/N_exists.con".
(* UNEXPORTED
-End N_Exists.
+End N_Exists
*)
(* UNEXPORTED
-Section Seq_is_CC_CAuchy.
+Section Seq_is_CC_CAuchy
*)
(*#* ** The Kneser sequence is Cauchy in [CC] *)
-inline "cic:/CoRN/fta/FTAreg/n.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/n.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/lt0n.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/lt0n.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/q.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/zleq.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zleq.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/qlt1.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/qlt1.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/c.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/c.var" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/zltc.var".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/zltc.var" "Seq_is_CC_CAuchy__".
(*#* %\begin{convention}% Let:
- [q_] prove [q[-]One [#] Zero]
(* begin hide *)
-inline "cic:/CoRN/fta/FTAreg/q_.con".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/q_.con" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/nrtq.con".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq.con" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/nrtc.con".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtc.con" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/nrtqlt1.con".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtqlt1.con" "Seq_is_CC_CAuchy__".
-inline "cic:/CoRN/fta/FTAreg/nrtq_.con".
+inline "cic:/CoRN/fta/FTAreg/Seq_is_CC_CAuchy/nrtq_.con" "Seq_is_CC_CAuchy__".
(* end hide *)
inline "cic:/CoRN/fta/FTAreg/seq_is_CC_Cauchy.con".
(* UNEXPORTED
-End Seq_is_CC_CAuchy.
+End Seq_is_CC_CAuchy
*)
inline "cic:/CoRN/fta/FTAreg/FTA_monic.con".
*)
(* UNEXPORTED
-Section Key_Lemma.
+Section Key_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/KeyLemma/a.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/n.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/n.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/gt_n_0.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/gt_n_0.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/eps.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/eps_pos.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_pos.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/a_nonneg.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_nonneg.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/a_n_1.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_n_1.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/a_0.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/a_0.var" "Key_Lemma__".
-inline "cic:/CoRN/fta/KeyLemma/eps_le_a_0.var".
+inline "cic:/CoRN/fta/KeyLemma/Key_Lemma/eps_le_a_0.var" "Key_Lemma__".
inline "cic:/CoRN/fta/KeyLemma/a_0_eps_nonneg.con".
(* end hide *)
(* UNEXPORTED
-End Key_Lemma.
+End Key_Lemma
*)
(* UNEXPORTED
(*#* ** Kneser Lemma *)
(* UNEXPORTED
-Section Kneser_Lemma.
+Section Kneser_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/KneserLemma/b.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b.var" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/n.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/n.var" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/gt_n_0.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/gt_n_0.var" "Kneser_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/fta/KneserLemma/b_0.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0.con" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/b_n.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n.con" "Kneser_Lemma__".
(* end hide *)
-inline "cic:/CoRN/fta/KneserLemma/b_n_1.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_n_1.var" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/c.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/c.var" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/b_0_lt_c.var".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/b_0_lt_c.var" "Kneser_Lemma__".
(*#*
%\begin{convention}% We define the following local abbreviations:
(* begin hide *)
-inline "cic:/CoRN/fta/KneserLemma/two_n.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/two_n.con" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/Small.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Small.con" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/Smaller.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smaller.con" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/Smallest.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/Smallest.con" "Kneser_Lemma__".
-inline "cic:/CoRN/fta/KneserLemma/q.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/q.con" "Kneser_Lemma__".
(* end hide *)
inline "cic:/CoRN/fta/KneserLemma/b_0'_exists.con".
-inline "cic:/CoRN/fta/KneserLemma/eta_0.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/eta_0.con" "Kneser_Lemma__".
inline "cic:/CoRN/fta/KneserLemma/eta_0_pos.con".
(* begin hide *)
-inline "cic:/CoRN/fta/KneserLemma/a.con".
+inline "cic:/CoRN/fta/KneserLemma/Kneser_Lemma/a.con" "Kneser_Lemma__".
(* end hide *)
inline "cic:/CoRN/fta/KneserLemma/Kneser_3.con".
(* UNEXPORTED
-End Kneser_Lemma.
+End Kneser_Lemma
*)
inline "cic:/CoRN/fta/KneserLemma/Kneser.con".
*)
(* UNEXPORTED
-Section Main_Lemma.
+Section Main_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/fta/MainLemma/a.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/n.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/n.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/gt_n_0.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/gt_n_0.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/eps.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/eps_pos.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_pos.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/a_nonneg.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_nonneg.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/a_n_1.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_n_1.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/a_0.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/a_0.var" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/eps_le_a_0.var".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/eps_le_a_0.var" "Main_Lemma__".
inline "cic:/CoRN/fta/MainLemma/a_0_pos.con".
(* begin hide *)
-inline "cic:/CoRN/fta/MainLemma/two_n.con".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/two_n.con" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/Small.con".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/Small.con" "Main_Lemma__".
-inline "cic:/CoRN/fta/MainLemma/Smaller.con".
+inline "cic:/CoRN/fta/MainLemma/Main_Lemma/Smaller.con" "Main_Lemma__".
(* end hide *)
(* end hide *)
(* UNEXPORTED
-End Main_Lemma.
+End Main_Lemma
*)
include "algebra/COrdCauchy.ma".
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* *Lemmas for Integration
refinement).
*)
-inline "cic:/CoRN/ftc/COrdLemmas/F.var".
+inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/F.var" "Lemmas__".
inline "cic:/CoRN/ftc/COrdLemmas/om_fun_lt.con".
(* begin hide *)
-inline "cic:/CoRN/ftc/COrdLemmas/f.var".
+inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f.var" "Lemmas__".
-inline "cic:/CoRN/ftc/COrdLemmas/f0.var".
+inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f0.var" "Lemmas__".
-inline "cic:/CoRN/ftc/COrdLemmas/f_mon.var".
+inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/f_mon.var" "Lemmas__".
-inline "cic:/CoRN/ftc/COrdLemmas/h.var".
+inline "cic:/CoRN/ftc/COrdLemmas/Lemmas/h.var" "Lemmas__".
(* end hide *)
(* begin hide *).con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section More_Lemmas.
+Section More_Lemmas
*)
-inline "cic:/CoRN/ftc/COrdLemmas/f'.con".
+inline "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/f'.con" "More_Lemmas__".
(* end hide *)
-inline "cic:/CoRN/ftc/COrdLemmas/F.var".
+inline "cic:/CoRN/ftc/COrdLemmas/More_Lemmas/F.var" "More_Lemmas__".
(* begin show *)
(* end hide *)
(* UNEXPORTED
-End More_Lemmas.
+End More_Lemmas
*)
*)
(* UNEXPORTED
-Section Various_Theorems.
+Section Various_Theorems
*)
(*#* *Calculus Theorems
inline "cic:/CoRN/ftc/CalculusTheorems/nexp_resp_leEq_odd.con".
(* UNEXPORTED
-End Various_Theorems.
+End Various_Theorems
*)
include "ftc/MoreFunctions.ma".
(* UNEXPORTED
-Section Maps_into_Compacts.
+Section Maps_into_Compacts
*)
(* UNEXPORTED
-Section Part_Funct.
+Section Part_Funct
*)
(*#* *Composition
partial functions, and prove some trivial results.
*)
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/F.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/G.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/a.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/a.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/b.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/b.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/Hab.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hab.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/c.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/c.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/d.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/d.var" "Maps_into_Compacts__Part_Funct__".
-inline "cic:/CoRN/ftc/Composition/Hcd.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hcd.var" "Maps_into_Compacts__Part_Funct__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Composition/I.con".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/I.con" "Maps_into_Compacts__Part_Funct__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/Hf.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/Hf.var" "Maps_into_Compacts__Part_Funct__".
(* end show *)
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/maps.var".
+inline "cic:/CoRN/ftc/Composition/Maps_into_Compacts/Part_Funct/maps.var" "Maps_into_Compacts__Part_Funct__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/maps_lemma_inc.con".
(* UNEXPORTED
-End Part_Funct.
+End Part_Funct
*)
(* UNEXPORTED
-End Maps_into_Compacts.
+End Maps_into_Compacts
*)
(* UNEXPORTED
-Section Mapping.
+Section Mapping
*)
(*#*
completely characterizes the domain of the composite function.
*)
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/F.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/G.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/a.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/a.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/b.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/b.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/Hab.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/Hab.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/c.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/c.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/d.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/d.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/Hcd.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/Hcd.var" "Mapping__".
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/Hf.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/Hf.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/Hg.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/Hg.var" "Mapping__".
-inline "cic:/CoRN/ftc/Composition/maps.var".
+inline "cic:/CoRN/ftc/Composition/Mapping/maps.var" "Mapping__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/included_comp.con".
(* UNEXPORTED
-End Mapping.
+End Mapping
*)
(* UNEXPORTED
-Section Interval_Continuity.
+Section Interval_Continuity
*)
(*#* **Continuity
We now prove that the composition of two continuous partial functions is continuous.
*)
-inline "cic:/CoRN/ftc/Composition/a.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/a.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/b.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/b.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/Hab.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hab.var" "Interval_Continuity__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Composition/I.con".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/I.con" "Interval_Continuity__".
(* end hide *)
-inline "cic:/CoRN/ftc/Composition/c.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/c.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/d.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/d.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/Hcd.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hcd.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/F.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/G.var" "Interval_Continuity__".
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/contF.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/contF.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/contG.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/contG.var" "Interval_Continuity__".
-inline "cic:/CoRN/ftc/Composition/Hmap.var".
+inline "cic:/CoRN/ftc/Composition/Interval_Continuity/Hmap.var" "Interval_Continuity__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/Continuous_I_comp.con".
(* UNEXPORTED
-End Interval_Continuity.
+End Interval_Continuity
*)
(* UNEXPORTED
-Section Derivative.
+Section Derivative
*)
(*#* **Derivative
We now work with the derivative relation and prove the chain rule for partial functions.
*)
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/F.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/F'.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/F'.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/G.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/G'.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/G'.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/a.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/a.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/b.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/b.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/Hab'.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/Hab'.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/c.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/c.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/d.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/d.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/Hcd'.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/Hcd'.var" "Derivative__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Composition/Hab.con".
+inline "cic:/CoRN/ftc/Composition/Derivative/Hab.con" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/Hcd.con".
+inline "cic:/CoRN/ftc/Composition/Derivative/Hcd.con" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/I.con".
+inline "cic:/CoRN/ftc/Composition/Derivative/I.con" "Derivative__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/derF.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/derF.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/derG.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/derG.var" "Derivative__".
-inline "cic:/CoRN/ftc/Composition/Hmap.var".
+inline "cic:/CoRN/ftc/Composition/Derivative/Hmap.var" "Derivative__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/Diffble_I_comp_aux.con".
(* UNEXPORTED
-End Derivative.
+End Derivative
*)
(* UNEXPORTED
-Section Differentiability.
+Section Differentiability
*)
(*#* **Differentiability
Finally, we move on to differentiability.
*)
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/F.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/G.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/a.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/a.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/b.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/b.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/Hab'.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/Hab'.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/c.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/c.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/d.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/d.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/Hcd'.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/Hcd'.var" "Differentiability__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Composition/Hab.con".
+inline "cic:/CoRN/ftc/Composition/Differentiability/Hab.con" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/Hcd.con".
+inline "cic:/CoRN/ftc/Composition/Differentiability/Hcd.con" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/I.con".
+inline "cic:/CoRN/ftc/Composition/Differentiability/I.con" "Differentiability__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/diffF.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/diffF.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/diffG.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/diffG.var" "Differentiability__".
-inline "cic:/CoRN/ftc/Composition/Hmap.var".
+inline "cic:/CoRN/ftc/Composition/Differentiability/Hmap.var" "Differentiability__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/Diffble_I_comp.con".
(* UNEXPORTED
-End Differentiability.
+End Differentiability
*)
(* UNEXPORTED
-Section Generalized_Intervals.
+Section Generalized_Intervals
*)
(*#* **Generalizations
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Composition/I.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/I.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/J.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/J.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/pI.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/pI.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/pJ.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/pJ.var" "Generalized_Intervals__".
inline "cic:/CoRN/ftc/Composition/maps_compacts_into.con".
inline "cic:/CoRN/ftc/Composition/comp_inc_lemma.con".
-inline "cic:/CoRN/ftc/Composition/F.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/F.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/F'.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/F'.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/G.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/G.var" "Generalized_Intervals__".
-inline "cic:/CoRN/ftc/Composition/G'.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/G'.var" "Generalized_Intervals__".
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/Hmap.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap.var" "Generalized_Intervals__".
(* end show *)
(* begin show *)
-inline "cic:/CoRN/ftc/Composition/Hmap'.var".
+inline "cic:/CoRN/ftc/Composition/Generalized_Intervals/Hmap'.var" "Generalized_Intervals__".
(* end show *)
inline "cic:/CoRN/ftc/Composition/Derivative_comp.con".
(* UNEXPORTED
-End Generalized_Intervals.
+End Generalized_Intervals
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
(*#*
inline "cic:/CoRN/ftc/Composition/Diffble_comp.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
include "ftc/FunctSums.ma".
(* UNEXPORTED
-Section Definitions_and_Basic_Results.
+Section Definitions_and_Basic_Results
*)
(*#* *Continuity
Here we define continuity and prove some basic properties of continuous functions.
*)
-inline "cic:/CoRN/ftc/Continuity/a.var".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/a.var" "Definitions_and_Basic_Results__".
-inline "cic:/CoRN/ftc/Continuity/b.var".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/b.var" "Definitions_and_Basic_Results__".
-inline "cic:/CoRN/ftc/Continuity/Hab.var".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hab.var" "Definitions_and_Basic_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/I.con".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/I.con" "Definitions_and_Basic_Results__".
(* end hide *)
-inline "cic:/CoRN/ftc/Continuity/F.var".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/F.var" "Definitions_and_Basic_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/P.con".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/P.con" "Definitions_and_Basic_Results__".
(* end hide *)
Assume [F] to be continuous in [I]. Then it has a least upper bound and a greater lower bound on [I].
*)
-inline "cic:/CoRN/ftc/Continuity/contF.var".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/contF.var" "Definitions_and_Basic_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/Hinc'.con".
+inline "cic:/CoRN/ftc/Continuity/Definitions_and_Basic_Results/Hinc'.con" "Definitions_and_Basic_Results__".
(* end hide *)
inline "cic:/CoRN/ftc/Continuity/less_Norm_Funct.con".
(* UNEXPORTED
-End Definitions_and_Basic_Results.
+End Definitions_and_Basic_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Local_Results.
+Section Local_Results
*)
(*#* **Algebraic Properties
We now state and prove some results about continuous functions. Assume that [I] is included in the domain of both [F] and [G].
*)
-inline "cic:/CoRN/ftc/Continuity/a.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/a.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/b.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/b.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/Hab.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/Hab.var" "Local_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/I.con".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/I.con" "Local_Results__".
(* end hide *)
-inline "cic:/CoRN/ftc/Continuity/F.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/F.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/G.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/G.var" "Local_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/P.con".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/P.con" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/Q.con".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/Q.con" "Local_Results__".
(* end hide *)
-inline "cic:/CoRN/ftc/Continuity/incF.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/incF.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/incG.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/incG.var" "Local_Results__".
(*#*
The first result does not require the function to be continuous; however, its preconditions are easily verified by continuous functions, which justifies its inclusion in this section.
Assume [F] and [G] are continuous in [I]. Then functions derived from these through algebraic operations are also continuous, provided (in the case of reciprocal and division) some extra conditions are met.
*)
-inline "cic:/CoRN/ftc/Continuity/contF.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/contF.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/contG.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/contG.var" "Local_Results__".
inline "cic:/CoRN/ftc/Continuity/Continuous_I_plus.con".
(* begin show *)
-inline "cic:/CoRN/ftc/Continuity/Hg'.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/Hg'.var" "Local_Results__".
-inline "cic:/CoRN/ftc/Continuity/Hg''.var".
+inline "cic:/CoRN/ftc/Continuity/Local_Results/Hg''.var" "Local_Results__".
(* end show *)
inline "cic:/CoRN/ftc/Continuity/Continuous_I_recip.con".
(* UNEXPORTED
-End Local_Results.
+End Local_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Corolaries.
+Section Corolaries
*)
-inline "cic:/CoRN/ftc/Continuity/a.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/a.var" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/b.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/b.var" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/Hab.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/Hab.var" "Corolaries__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/I.con".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/I.con" "Corolaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/Continuity/F.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/F.var" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/G.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/G.var" "Corolaries__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/P.con".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/P.con" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/Q.con".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/Q.con" "Corolaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/Continuity/contF.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/contF.var" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/contG.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/contG.var" "Corolaries__".
(*#*
The corresponding properties for subtraction, division and
inline "cic:/CoRN/ftc/Continuity/Continuous_I_abs.con".
-inline "cic:/CoRN/ftc/Continuity/Hg'.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/Hg'.var" "Corolaries__".
-inline "cic:/CoRN/ftc/Continuity/Hg''.var".
+inline "cic:/CoRN/ftc/Continuity/Corolaries/Hg''.var" "Corolaries__".
inline "cic:/CoRN/ftc/Continuity/Continuous_I_div.con".
(* UNEXPORTED
-End Corolaries.
+End Corolaries
*)
(* UNEXPORTED
-Section Other.
+Section Other
*)
(* UNEXPORTED
-Section Sums.
+Section Sums
*)
(*#*
We finally prove that the sum of an arbitrary family of continuous functions is still a continuous function.
*)
-inline "cic:/CoRN/ftc/Continuity/a.var".
+inline "cic:/CoRN/ftc/Continuity/Other/Sums/a.var" "Other__Sums__".
-inline "cic:/CoRN/ftc/Continuity/b.var".
+inline "cic:/CoRN/ftc/Continuity/Other/Sums/b.var" "Other__Sums__".
-inline "cic:/CoRN/ftc/Continuity/Hab.var".
+inline "cic:/CoRN/ftc/Continuity/Other/Sums/Hab.var" "Other__Sums__".
-inline "cic:/CoRN/ftc/Continuity/Hab'.var".
+inline "cic:/CoRN/ftc/Continuity/Other/Sums/Hab'.var" "Other__Sums__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Continuity/I.con".
+inline "cic:/CoRN/ftc/Continuity/Other/Sums/I.con" "Other__Sums__".
(* end hide *)
inline "cic:/CoRN/ftc/Continuity/Continuous_I_Sum.con".
(* UNEXPORTED
-End Sums.
+End Sums
*)
(*#*
inline "cic:/CoRN/ftc/Continuity/included_imp_norm_leEq.con".
(* UNEXPORTED
-End Other.
+End Other
*)
(* UNEXPORTED
include "ftc/Continuity.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Derivatives
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Derivative/a.var".
+inline "cic:/CoRN/ftc/Derivative/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/ftc/Derivative/b.var".
+inline "cic:/CoRN/ftc/Derivative/Definitions/b.var" "Definitions__".
-inline "cic:/CoRN/ftc/Derivative/Hab'.var".
+inline "cic:/CoRN/ftc/Derivative/Definitions/Hab'.var" "Definitions__".
(* 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".
+inline "cic:/CoRN/ftc/Derivative/Definitions/F.var" "Definitions__".
(* 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".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#* **Basic Properties
*)
-inline "cic:/CoRN/ftc/Derivative/a.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/a.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Derivative/b.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/b.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Derivative/Hab'.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab'.var" "Basic_Properties__".
(* 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 *)
Derivative is a well defined relation; we will make this explicit for both arguments:
*)
-inline "cic:/CoRN/ftc/Derivative/F.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/F.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Derivative/G.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/G.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Derivative/H.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/H.var" "Basic_Properties__".
(* 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 *)
(* 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 *)
Any function that is or has a derivative is continuous.
*)
-inline "cic:/CoRN/ftc/Derivative/Hab''.var".
+inline "cic:/CoRN/ftc/Derivative/Basic_Properties/Hab''.var" "Basic_Properties__".
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
*)
(*#*
include "ftc/Derivative.ma".
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* **Algebraic Operations
We begin with some technical stuff that will be necessary for division.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/a.var" "Lemmas__".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/b.var" "Lemmas__".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Hab.var" "Lemmas__".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/I.con" "Lemmas__".
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/F.var" "Lemmas__".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/P.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/P.con" "Lemmas__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Lemmas/Fbnd.var" "Lemmas__".
(* end show *)
inline "cic:/CoRN/ftc/DerivativeOps/bnd_away_zero_square.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Local_Results.
+Section Local_Results
*)
(*#* **Local Results
We can now derive all the usual rules for deriving constant and identity functions, sums, inverses and products of functions with a known derivative.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/a.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/b.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab'.var" "Local_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Hab.con" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/I.con" "Local_Results__".
(* end hide *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_id.con".
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/F'.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/G.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/G'.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derF.var" "Local_Results__".
-inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/derG.var" "Local_Results__".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_plus.con".
(* begin show *)
-inline "cic:/CoRN/ftc/DerivativeOps/Fbnd.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Local_Results/Fbnd.var" "Local_Results__".
(* end show *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_recip.con".
(* UNEXPORTED
-End Local_Results.
+End Local_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Corolaries.
+Section Corolaries
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/a.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/b.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab'.var" "Corolaries__".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Hab.con" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/I.con" "Corolaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/F.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/F'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/F'.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/G.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/G'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/G'.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/derF.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derF.var" "Corolaries__".
-inline "cic:/CoRN/ftc/DerivativeOps/derG.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/derG.var" "Corolaries__".
(*#*
From this lemmas the rules for the other algebraic operations follow directly.
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_nth.con".
-inline "cic:/CoRN/ftc/DerivativeOps/Gbnd.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Corolaries/Gbnd.var" "Corolaries__".
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_div.con".
(* UNEXPORTED
-End Corolaries.
+End Corolaries
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Derivative_Sums.
+Section Derivative_Sums
*)
(*#* The derivation rules for families of functions are easily proved by
induction using the constant and addition rules.
*)
-inline "cic:/CoRN/ftc/DerivativeOps/a.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/a.var" "Derivative_Sums__".
-inline "cic:/CoRN/ftc/DerivativeOps/b.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/b.var" "Derivative_Sums__".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab.var" "Derivative_Sums__".
-inline "cic:/CoRN/ftc/DerivativeOps/Hab'.var".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/Hab'.var" "Derivative_Sums__".
(* begin hide *)
-inline "cic:/CoRN/ftc/DerivativeOps/I.con".
+inline "cic:/CoRN/ftc/DerivativeOps/Derivative_Sums/I.con" "Derivative_Sums__".
(* end hide *)
inline "cic:/CoRN/ftc/DerivativeOps/Derivative_I_Sum.con".
(* UNEXPORTED
-End Derivative_Sums.
+End Derivative_Sums
*)
(* UNEXPORTED
include "ftc/DerivativeOps.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Differentiability
inline "cic:/CoRN/ftc/Differentiability/Diffble_I.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Local_Properties.
+Section Local_Properties
*)
(*#*
A function differentiable in an interval is everywhere defined in that interval.
*)
-inline "cic:/CoRN/ftc/Differentiability/a.var".
+inline "cic:/CoRN/ftc/Differentiability/Local_Properties/a.var" "Local_Properties__".
-inline "cic:/CoRN/ftc/Differentiability/b.var".
+inline "cic:/CoRN/ftc/Differentiability/Local_Properties/b.var" "Local_Properties__".
-inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
+inline "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab'.var" "Local_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Differentiability/Hab.con".
+inline "cic:/CoRN/ftc/Differentiability/Local_Properties/Hab.con" "Local_Properties__".
-inline "cic:/CoRN/ftc/Differentiability/I.con".
+inline "cic:/CoRN/ftc/Differentiability/Local_Properties/I.con" "Local_Properties__".
(* end hide *)
inline "cic:/CoRN/ftc/Differentiability/deriv_imp_Diffble_I.con".
(* UNEXPORTED
-End Local_Properties.
+End Local_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(*#*
All the algebraic results carry on.
*)
-inline "cic:/CoRN/ftc/Differentiability/a.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/a.var" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/b.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/b.var" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Hab'.var" "Operations__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Differentiability/Hab.con".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Hab.con" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/I.con".
+inline "cic:/CoRN/ftc/Differentiability/Operations/I.con" "Operations__".
(* end hide *)
(* UNEXPORTED
-Section Constants.
+Section Constants
*)
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_const.con".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_id.con".
(* UNEXPORTED
-End Constants.
+End Constants
*)
(* UNEXPORTED
-Section Well_Definedness.
+Section Well_Definedness
*)
-inline "cic:/CoRN/ftc/Differentiability/F.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/F.var" "Operations__Well_Definedness__".
-inline "cic:/CoRN/ftc/Differentiability/H.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/H.var" "Operations__Well_Definedness__".
-inline "cic:/CoRN/ftc/Differentiability/diffF.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Well_Definedness/diffF.var" "Operations__Well_Definedness__".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_wd.con".
(* UNEXPORTED
-End Well_Definedness.
+End Well_Definedness
*)
-inline "cic:/CoRN/ftc/Differentiability/F.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/F.var" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/G.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/G.var" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/diffF.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/diffF.var" "Operations__".
-inline "cic:/CoRN/ftc/Differentiability/diffG.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/diffG.var" "Operations__".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_plus.con".
(* begin show *)
-inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
+inline "cic:/CoRN/ftc/Differentiability/Operations/Gbnd.var" "Operations__".
(* end show *)
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_recip.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/Differentiability/a.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/a.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/b.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/b.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/Hab'.var" "Corollaries__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Differentiability/Hab.con".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/Hab.con" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/I.con".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/I.con" "Corollaries__".
(* end hide *)
-inline "cic:/CoRN/ftc/Differentiability/F.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/F.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/G.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/G.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/diffF.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/diffF.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Differentiability/diffG.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/diffG.var" "Corollaries__".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_minus.con".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_nth.con".
-inline "cic:/CoRN/ftc/Differentiability/Gbnd.var".
+inline "cic:/CoRN/ftc/Differentiability/Corollaries/Gbnd.var" "Corollaries__".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_div.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-Section Other_Properties.
+Section Other_Properties
*)
(*#*
induction using the constant and addition rules.
*)
-inline "cic:/CoRN/ftc/Differentiability/a.var".
+inline "cic:/CoRN/ftc/Differentiability/Other_Properties/a.var" "Other_Properties__".
-inline "cic:/CoRN/ftc/Differentiability/b.var".
+inline "cic:/CoRN/ftc/Differentiability/Other_Properties/b.var" "Other_Properties__".
-inline "cic:/CoRN/ftc/Differentiability/Hab'.var".
+inline "cic:/CoRN/ftc/Differentiability/Other_Properties/Hab'.var" "Other_Properties__".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum0.con".
inline "cic:/CoRN/ftc/Differentiability/Diffble_I_Sum.con".
(* UNEXPORTED
-End Other_Properties.
+End Other_Properties
*)
(*#*
*)
(* UNEXPORTED
-Section Indefinite_Integral.
+Section Indefinite_Integral
*)
(*#* *The Fundamental Theorem of Calculus
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/FTC/I.var".
+inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/I.var" "Indefinite_Integral__".
-inline "cic:/CoRN/ftc/FTC/F.var".
+inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/F.var" "Indefinite_Integral__".
-inline "cic:/CoRN/ftc/FTC/contF.var".
+inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/contF.var" "Indefinite_Integral__".
-inline "cic:/CoRN/ftc/FTC/a.var".
+inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/a.var" "Indefinite_Integral__".
-inline "cic:/CoRN/ftc/FTC/Ha.var".
+inline "cic:/CoRN/ftc/FTC/Indefinite_Integral/Ha.var" "Indefinite_Integral__".
inline "cic:/CoRN/ftc/FTC/prim_lemma.con".
inline "cic:/CoRN/ftc/FTC/Fprim.con".
(* UNEXPORTED
-End Indefinite_Integral.
+End Indefinite_Integral
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section FTC.
+Section FTC
*)
(*#* **The FTC
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/FTC/J.var".
+inline "cic:/CoRN/ftc/FTC/FTC/J.var" "FTC__".
-inline "cic:/CoRN/ftc/FTC/F.var".
+inline "cic:/CoRN/ftc/FTC/FTC/F.var" "FTC__".
-inline "cic:/CoRN/ftc/FTC/contF.var".
+inline "cic:/CoRN/ftc/FTC/FTC/contF.var" "FTC__".
-inline "cic:/CoRN/ftc/FTC/x0.var".
+inline "cic:/CoRN/ftc/FTC/FTC/x0.var" "FTC__".
-inline "cic:/CoRN/ftc/FTC/Hx0.var".
+inline "cic:/CoRN/ftc/FTC/FTC/Hx0.var" "FTC__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FTC/G.con".
+inline "cic:/CoRN/ftc/FTC/FTC/G.con" "FTC__".
(* end hide *)
The derivative of [G] is simply [F].
*)
-inline "cic:/CoRN/ftc/FTC/pJ.var".
+inline "cic:/CoRN/ftc/FTC/FTC/pJ.var" "FTC__".
inline "cic:/CoRN/ftc/FTC/FTC1.con".
Any other function [G0] with derivative [F] must differ from [G] by a constant.
*)
-inline "cic:/CoRN/ftc/FTC/G0.var".
+inline "cic:/CoRN/ftc/FTC/FTC/G0.var" "FTC__".
-inline "cic:/CoRN/ftc/FTC/derG0.var".
+inline "cic:/CoRN/ftc/FTC/FTC/derG0.var" "FTC__".
inline "cic:/CoRN/ftc/FTC/FTC2.con".
(* begin hide *)
-inline "cic:/CoRN/ftc/FTC/G0_inc.con".
+inline "cic:/CoRN/ftc/FTC/FTC/G0_inc.con" "FTC__".
(* end hide *)
(* end hide *)
(* UNEXPORTED
-End FTC.
+End FTC
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Limit_of_Integral_Seq.
+Section Limit_of_Integral_Seq
*)
(*#* **Corollaries
commutes with the indefinite integral.
*)
-inline "cic:/CoRN/ftc/FTC/J.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/J.var" "Limit_of_Integral_Seq__".
-inline "cic:/CoRN/ftc/FTC/f.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/f.var" "Limit_of_Integral_Seq__".
-inline "cic:/CoRN/ftc/FTC/F.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/F.var" "Limit_of_Integral_Seq__".
-inline "cic:/CoRN/ftc/FTC/contf.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contf.var" "Limit_of_Integral_Seq__".
-inline "cic:/CoRN/ftc/FTC/contF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/contF.var" "Limit_of_Integral_Seq__".
(* UNEXPORTED
-Section Compact.
+Section Compact
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/FTC/a.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/a.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/b.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/b.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/Hab.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hab.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/contIf.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIf.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/contIF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contIF.var" "Limit_of_Integral_Seq__Compact__".
(* begin show *)
-inline "cic:/CoRN/ftc/FTC/convF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/convF.var" "Limit_of_Integral_Seq__Compact__".
(* end show *)
-inline "cic:/CoRN/ftc/FTC/x0.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/x0.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/Hx0.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/Hx0'.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/Hx0'.var" "Limit_of_Integral_Seq__Compact__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FTC/g.con".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/g.con" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/G.con".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/G.con" "Limit_of_Integral_Seq__Compact__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/FTC/contg.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contg.var" "Limit_of_Integral_Seq__Compact__".
-inline "cic:/CoRN/ftc/FTC/contG.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/Compact/contG.var" "Limit_of_Integral_Seq__Compact__".
(* end show *)
inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral.con".
(* UNEXPORTED
-End Compact.
+End Compact
*)
(*#*
inline "cic:/CoRN/ftc/FTC/limit_of_Integral.con".
(* UNEXPORTED
-Section General.
+Section General
*)
(*#*
(* begin show *)
-inline "cic:/CoRN/ftc/FTC/convF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/convF.var" "Limit_of_Integral_Seq__General__".
(* end show *)
-inline "cic:/CoRN/ftc/FTC/x0.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/x0.var" "Limit_of_Integral_Seq__General__".
-inline "cic:/CoRN/ftc/FTC/Hx0.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/Hx0.var" "Limit_of_Integral_Seq__General__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FTC/g.con".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/g.con" "Limit_of_Integral_Seq__General__".
-inline "cic:/CoRN/ftc/FTC/G.con".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/G.con" "Limit_of_Integral_Seq__General__".
(* end hide *)
-inline "cic:/CoRN/ftc/FTC/contg.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contg.var" "Limit_of_Integral_Seq__General__".
-inline "cic:/CoRN/ftc/FTC/contG.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Integral_Seq/General/contG.var" "Limit_of_Integral_Seq__General__".
inline "cic:/CoRN/ftc/FTC/fun_lim_seq_integral_IR.con".
(* UNEXPORTED
-End General.
+End General
*)
(* UNEXPORTED
-End Limit_of_Integral_Seq.
+End Limit_of_Integral_Seq
*)
(* UNEXPORTED
-Section Limit_of_Derivative_Seq.
+Section Limit_of_Derivative_Seq
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/FTC/J.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/J.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/pJ.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/pJ.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/f.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/f.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/g.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/g.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/F.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/F.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/G.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/G.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/contf.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contf.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/contF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contF.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/convF.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convF.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/contg.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contg.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/contG.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/contG.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/convG.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/convG.var" "Limit_of_Derivative_Seq__".
-inline "cic:/CoRN/ftc/FTC/derf.var".
+inline "cic:/CoRN/ftc/FTC/Limit_of_Derivative_Seq/derf.var" "Limit_of_Derivative_Seq__".
inline "cic:/CoRN/ftc/FTC/fun_lim_seq_derivative.con".
(* UNEXPORTED
-End Limit_of_Derivative_Seq.
+End Limit_of_Derivative_Seq
*)
(* UNEXPORTED
-Section Derivative_Series.
+Section Derivative_Series
*)
(*#*
As a very important case of this result, we get a rule for deriving series.
*)
-inline "cic:/CoRN/ftc/FTC/J.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/J.var" "Derivative_Series__".
-inline "cic:/CoRN/ftc/FTC/pJ.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/pJ.var" "Derivative_Series__".
-inline "cic:/CoRN/ftc/FTC/f.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/f.var" "Derivative_Series__".
-inline "cic:/CoRN/ftc/FTC/g.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/g.var" "Derivative_Series__".
(* begin show *)
-inline "cic:/CoRN/ftc/FTC/convF.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/convF.var" "Derivative_Series__".
-inline "cic:/CoRN/ftc/FTC/convG.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/convG.var" "Derivative_Series__".
(* end show *)
-inline "cic:/CoRN/ftc/FTC/derF.var".
+inline "cic:/CoRN/ftc/FTC/Derivative_Series/derF.var" "Derivative_Series__".
inline "cic:/CoRN/ftc/FTC/Derivative_FSeries.con".
(* UNEXPORTED
-End Derivative_Series.
+End Derivative_Series
*)
include "ftc/PartInterval.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Sequences of Functions
see Bishop 1967.
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/b.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/Hab.var" "Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/I.con" "Definitions__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/f.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/F.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/F.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/contf.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/contF.var".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/contF.var" "Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/incf.con".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/incf.con" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/incF.con".
+inline "cic:/CoRN/ftc/FunctSequence/Definitions/incF.con" "Definitions__".
(* end hide *)
inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_real.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/a.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/b.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/Hab.var" "More_Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/I.con" "More_Definitions__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/f.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/contf.var" "More_Definitions__".
(*#*
We can also say that [f] is simply convergent if it converges to some
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/H.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Definitions/H.var" "More_Definitions__".
(* end show *)
inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq_Lim.con".
(* UNEXPORTED
-End More_Definitions.
+End More_Definitions
*)
(* UNEXPORTED
-Section Irrelevance_of_Proofs.
+Section Irrelevance_of_Proofs
*)
(*#* **Irrelevance of Proofs
This section contains a number of technical results stating mainly that being a Cauchy sequence or converging to some limit is a property of the sequence itself and independent of the proofs we supply of its continuity or the continuity of its limit.
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/a.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/b.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/Hab.var" "Irrelevance_of_Proofs__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/I.con" "Irrelevance_of_Proofs__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/f.var" "Irrelevance_of_Proofs__".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/FunctSequence/contf0.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contf0.var" "Irrelevance_of_Proofs__".
(* end show *)
-inline "cic:/CoRN/ftc/FunctSequence/F.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/F.var" "Irrelevance_of_Proofs__".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/contF.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/FunctSequence/contF0.var".
+inline "cic:/CoRN/ftc/FunctSequence/Irrelevance_of_Proofs/contF0.var" "Irrelevance_of_Proofs__".
(* end show *)
inline "cic:/CoRN/ftc/FunctSequence/Cauchy_fun_seq1_wd.con".
(* UNEXPORTED
-End Irrelevance_of_Proofs.
+End Irrelevance_of_Proofs
*)
(* UNEXPORTED
-Section More_Proof_Irrelevance.
+Section More_Proof_Irrelevance
*)
inline "cic:/CoRN/ftc/FunctSequence/conv_fun_seq_wd.con".
(* UNEXPORTED
-End More_Proof_Irrelevance.
+End More_Proof_Irrelevance
*)
(* UNEXPORTED
-Section More_Properties.
+Section More_Properties
*)
(*#* **Other Properties
defined with respect to functional equality in the interval [[a,b]].
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/a.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/b.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/Hab.var" "More_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/I.con" "More_Properties__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/f.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/g.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/g.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contf.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contf0.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contf0.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contg.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contg.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contg0.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contg0.var" "More_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/FunctSequence/Cauchy_conv_fun_seq'.con".
-inline "cic:/CoRN/ftc/FunctSequence/F.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/F.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/G.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/G.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/contF.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contF.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contF0.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contF0.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contG.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contG.var" "More_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contG0.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Properties/contG0.var" "More_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/FunctSequence/seq_conv_imp_fun_conv.con".
(* UNEXPORTED
-End More_Properties.
+End More_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Algebraic_Properties.
+Section Algebraic_Properties
*)
(*#* **Algebraic Properties
We now study how convergence is affected by algebraic operations, and some algebraic properties of the limit function.
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/a.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/b.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/Hab.var" "Algebraic_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/I.con" "Algebraic_Properties__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/f.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/g.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/g.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contf.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contg.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contg.var" "Algebraic_Properties__".
(*#*
First, the limit function is unique.
We now prove that if two sequences converge than their sum (difference, product) also converge to the sum (difference, product) of their limits.
*)
-inline "cic:/CoRN/ftc/FunctSequence/F.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/F.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/G.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/G.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contF.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contF.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contG.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/contG.var" "Algebraic_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSequence/convF.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convF.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/convG.var".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/convG.var" "Algebraic_Properties__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/incf.con".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incf.con" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/incg.con".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incg.con" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/incF.con".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incF.con" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/incG.con".
+inline "cic:/CoRN/ftc/FunctSequence/Algebraic_Properties/incG.con" "Algebraic_Properties__".
(* end hide *)
inline "cic:/CoRN/ftc/FunctSequence/fun_Lim_seq_mult'.con".
(* UNEXPORTED
-End Algebraic_Properties.
+End Algebraic_Properties
*)
(* UNEXPORTED
-Section More_Algebraic_Properties.
+Section More_Algebraic_Properties
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/a.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/b.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hab.var" "More_Algebraic_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/I.con" "More_Algebraic_Properties__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/f.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/g.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/g.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contf.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contg.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/contg.var" "More_Algebraic_Properties__".
(*#*
The same is true if we don't make the limits explicit.
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/Hf.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hf.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hg.var".
+inline "cic:/CoRN/ftc/FunctSequence/More_Algebraic_Properties/Hg.var" "More_Algebraic_Properties__".
(* end hide *)
inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_mult.con".
(* UNEXPORTED
-End More_Algebraic_Properties.
+End More_Algebraic_Properties
*)
(* UNEXPORTED
-Section Still_More_Algebraic_Properties.
+Section Still_More_Algebraic_Properties
*)
-inline "cic:/CoRN/ftc/FunctSequence/a.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/a.var" "Still_More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/b.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/b.var" "Still_More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hab.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hab.var" "Still_More_Algebraic_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSequence/I.con".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/I.con" "Still_More_Algebraic_Properties__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSequence/f.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/f.var" "Still_More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/contf.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/contf.var" "Still_More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/FunctSequence/Hf.var".
+inline "cic:/CoRN/ftc/FunctSequence/Still_More_Algebraic_Properties/Hf.var" "Still_More_Algebraic_Properties__".
(*#*
As a corollary, we get the analogous property for the sequence of algebraic inverse functions.
inline "cic:/CoRN/ftc/FunctSequence/fun_Cauchy_prop_inv.con".
(* UNEXPORTED
-End Still_More_Algebraic_Properties.
+End Still_More_Algebraic_Properties
*)
(* UNEXPORTED
(*#* printing Fun_Series_Sum %\ensuremath{\sum_0^{\infty}}% #∑<sub>0</sub><sup>∞</sup># *)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Series of Functions
convergence is simply the convergence of the sequence of partial sums.
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/b.var" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/Hab.var" "Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSeries/I.con".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/I.con" "Definitions__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/f.var" "Definitions__".
inline "cic:/CoRN/ftc/FunctSeries/fun_seq_part_sum.con".
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSeries/H.var".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/H.var" "Definitions__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSeries/contf.con".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/contf.con" "Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/incf.con".
+inline "cic:/CoRN/ftc/FunctSeries/Definitions/incf.con" "Definitions__".
(* end hide *)
inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/a.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/b.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/Hab.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Definitions/f.var" "More_Definitions__".
(*#* A series can also be absolutely convergent. *)
inline "cic:/CoRN/ftc/FunctSeries/fun_series_abs_convergent.con".
(* UNEXPORTED
-End More_Definitions.
+End More_Definitions
*)
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(* **Algebraic Properties
All of these are analogous to the properties for series of real numbers, so we won't comment much about them.
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/a.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/b.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/Hab.var" "Operations__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSeries/I.con".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/I.con" "Operations__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/f.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/g.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/g.var" "Operations__".
(* end show *)
(* begin show *)
-inline "cic:/CoRN/ftc/FunctSeries/convF.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/convF.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/convG.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/convG.var" "Operations__".
(* end show *)
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/FunctSeries/c.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/c.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/H.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/H.var" "Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/contH.var".
+inline "cic:/CoRN/ftc/FunctSeries/Operations/contH.var" "Operations__".
inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_scal.con".
inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_scal.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(* UNEXPORTED
-Section More_Operations.
+Section More_Operations
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/a.var" "More_Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/b.var" "More_Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/Hab.var" "More_Operations__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSeries/I.con".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/I.con" "More_Operations__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/f.var" "More_Operations__".
-inline "cic:/CoRN/ftc/FunctSeries/convF.var".
+inline "cic:/CoRN/ftc/FunctSeries/More_Operations/convF.var" "More_Operations__".
inline "cic:/CoRN/ftc/FunctSeries/conv_fun_series_inv.con".
inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_inv.con".
(* UNEXPORTED
-End More_Operations.
+End More_Operations
*)
(* UNEXPORTED
-Section Other_Results.
+Section Other_Results
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/Other_Results/a.var" "Other_Results__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/Other_Results/b.var" "Other_Results__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/Other_Results/Hab.var" "Other_Results__".
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/Other_Results/f.var" "Other_Results__".
-inline "cic:/CoRN/ftc/FunctSeries/convF.var".
+inline "cic:/CoRN/ftc/FunctSeries/Other_Results/convF.var" "Other_Results__".
(*#*
The following relate the sum series with the limit of the sequence of
inline "cic:/CoRN/ftc/FunctSeries/Fun_Series_Sum_as_Lim.con".
(* UNEXPORTED
-End Other_Results.
+End Other_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Convergence_Criteria.
+Section Convergence_Criteria
*)
(*#* **Convergence Criteria
Most of the convergence criteria for series of real numbers carry over to series of real-valued functions, so again we just present them without comments.
*)
-inline "cic:/CoRN/ftc/FunctSeries/a.var".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/a.var" "Convergence_Criteria__".
-inline "cic:/CoRN/ftc/FunctSeries/b.var".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/b.var" "Convergence_Criteria__".
-inline "cic:/CoRN/ftc/FunctSeries/Hab.var".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/Hab.var" "Convergence_Criteria__".
(* begin hide *)
-inline "cic:/CoRN/ftc/FunctSeries/I.con".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/I.con" "Convergence_Criteria__".
(* end hide *)
-inline "cic:/CoRN/ftc/FunctSeries/f.var".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/f.var" "Convergence_Criteria__".
-inline "cic:/CoRN/ftc/FunctSeries/contF.var".
+inline "cic:/CoRN/ftc/FunctSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__".
(* UNEXPORTED
Opaque Frestr.
inline "cic:/CoRN/ftc/FunctSeries/fun_ratio_test_conv.con".
(* UNEXPORTED
-End Convergence_Criteria.
+End Convergence_Criteria
*)
(* begin hide *)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
-inline "cic:/CoRN/ftc/Integral/Sumx_wd_weird.con".
+inline "cic:/CoRN/ftc/Integral/Lemmas/Sumx_wd_weird.con" "Lemmas__".
inline "cic:/CoRN/ftc/Integral/Sumx_weird_lemma.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* end hide *)
(* UNEXPORTED
-Section Integral.
+Section Integral
*)
(*#* *Integral
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/a.var".
+inline "cic:/CoRN/ftc/Integral/Integral/a.var" "Integral__".
-inline "cic:/CoRN/ftc/Integral/b.var".
+inline "cic:/CoRN/ftc/Integral/Integral/b.var" "Integral__".
-inline "cic:/CoRN/ftc/Integral/Hab.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Hab.var" "Integral__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/I.con".
+inline "cic:/CoRN/ftc/Integral/Integral/I.con" "Integral__".
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Integral/F.var" "Integral__".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+inline "cic:/CoRN/ftc/Integral/Integral/contF.var" "Integral__".
-inline "cic:/CoRN/ftc/Integral/contF'.con".
+inline "cic:/CoRN/ftc/Integral/Integral/contF'.con" "Integral__".
(* end hide *)
(* UNEXPORTED
-Section Darboux_Sum.
+Section Darboux_Sum
*)
inline "cic:/CoRN/ftc/Integral/integral_seq.con".
inline "cic:/CoRN/ftc/Integral/integral.con".
(* UNEXPORTED
-End Darboux_Sum.
+End Darboux_Sum
*)
(* UNEXPORTED
-Section Integral_Thm.
+Section Integral_Thm
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/n.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/n.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/P.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/P.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/e.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/e.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/He.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/He.var" "Integral__Integral_Thm__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/d.con".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/d.con" "Integral__Integral_Thm__".
(* end hide *)
-inline "cic:/CoRN/ftc/Integral/HmeshP.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HmeshP.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/fP.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/fP.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/HfP.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/HfP'.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/HfP'.var" "Integral__Integral_Thm__".
-inline "cic:/CoRN/ftc/Integral/incF.var".
+inline "cic:/CoRN/ftc/Integral/Integral/Integral_Thm/incF.var" "Integral__Integral_Thm__".
inline "cic:/CoRN/ftc/Integral/partition_Sum_conv_integral.con".
(* UNEXPORTED
-End Integral_Thm.
+End Integral_Thm
*)
(* UNEXPORTED
-End Integral.
+End Integral
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#*
The usual extensionality and strong extensionality results hold.
*)
-inline "cic:/CoRN/ftc/Integral/a.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/a.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Integral/b.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/b.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/Integral/Hab.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Hab.var" "Basic_Properties__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/I.con".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/I.con" "Basic_Properties__".
(* end hide *)
*)
(* UNEXPORTED
-Section Well_Definedness.
+Section Well_Definedness
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/F.var" "Basic_Properties__Well_Definedness__".
-inline "cic:/CoRN/ftc/Integral/G.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/G.var" "Basic_Properties__Well_Definedness__".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contF.var" "Basic_Properties__Well_Definedness__".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Well_Definedness/contG.var" "Basic_Properties__Well_Definedness__".
inline "cic:/CoRN/ftc/Integral/integral_strext.con".
inline "cic:/CoRN/ftc/Integral/integral_wd'.con".
(* UNEXPORTED
-End Well_Definedness.
+End Well_Definedness
*)
(* UNEXPORTED
-Section Linearity_and_Monotonicity.
+Section Linearity_and_Monotonicity
*)
(* UNEXPORTED
inline "cic:/CoRN/ftc/Integral/integral_one.con".
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/F.var" "Basic_Properties__Linearity_and_Monotonicity__".
-inline "cic:/CoRN/ftc/Integral/G.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/G.var" "Basic_Properties__Linearity_and_Monotonicity__".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contF.var" "Basic_Properties__Linearity_and_Monotonicity__".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity/contG.var" "Basic_Properties__Linearity_and_Monotonicity__".
inline "cic:/CoRN/ftc/Integral/integral_comm_scal.con".
inline "cic:/CoRN/ftc/Integral/integral_empty.con".
(* UNEXPORTED
-End Linearity_and_Monotonicity.
+End Linearity_and_Monotonicity
*)
(* UNEXPORTED
-Section Linearity_and_Monotonicity'.
+Section Linearity_and_Monotonicity'
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/F.var" "Basic_Properties__Linearity_and_Monotonicity'__".
-inline "cic:/CoRN/ftc/Integral/G.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/G.var" "Basic_Properties__Linearity_and_Monotonicity'__".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contF.var" "Basic_Properties__Linearity_and_Monotonicity'__".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contG.var" "Basic_Properties__Linearity_and_Monotonicity'__".
(*#*
%\begin{convention}% Let [alpha, beta : IR] and assume that
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/alpha.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/alpha.var" "Basic_Properties__Linearity_and_Monotonicity'__".
-inline "cic:/CoRN/ftc/Integral/beta.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/beta.var" "Basic_Properties__Linearity_and_Monotonicity'__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Integral/h.con".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/h.con" "Basic_Properties__Linearity_and_Monotonicity'__".
(* end hide *)
-inline "cic:/CoRN/ftc/Integral/contH.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Linearity_and_Monotonicity'/contH.var" "Basic_Properties__Linearity_and_Monotonicity'__".
inline "cic:/CoRN/ftc/Integral/linear_integral.con".
*)
(* UNEXPORTED
-End Linearity_and_Monotonicity'.
+End Linearity_and_Monotonicity'
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/F.var" "Basic_Properties__Corollaries__".
-inline "cic:/CoRN/ftc/Integral/G.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/G.var" "Basic_Properties__Corollaries__".
-inline "cic:/CoRN/ftc/Integral/contF.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contF.var" "Basic_Properties__Corollaries__".
-inline "cic:/CoRN/ftc/Integral/contG.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Corollaries/contG.var" "Basic_Properties__Corollaries__".
(*#*
As corollaries we can calculate integrals of group operations applied to functions.
inline "cic:/CoRN/ftc/Integral/integral_leEq_norm.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-Section Integral_Sum.
+Section Integral_Sum
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/F.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/F.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/c.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/c.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/Hac.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/Hcb.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/Hab'.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hab'.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/Hac'.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hac'.var" "Basic_Properties__Integral_Sum__".
-inline "cic:/CoRN/ftc/Integral/Hcb'.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Hcb'.var" "Basic_Properties__Integral_Sum__".
(* UNEXPORTED
-Section Partition_Join.
+Section Partition_Join
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/n.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/n.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/m.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/m.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/P.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/P.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/Q.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/Q.var" "Basic_Properties__Integral_Sum__Partition_Join__".
(* begin hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Integral/fP.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fP.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/HfP.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/HfP'.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfP'.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/fQ.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/fQ.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/HfQ.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ.var" "Basic_Properties__Integral_Sum__Partition_Join__".
-inline "cic:/CoRN/ftc/Integral/HfQ'.var".
+inline "cic:/CoRN/ftc/Integral/Basic_Properties/Integral_Sum/Partition_Join/HfQ'.var" "Basic_Properties__Integral_Sum__Partition_Join__".
(* begin hide *)
inline "cic:/CoRN/ftc/Integral/partition_join_mesh.con".
(* UNEXPORTED
-End Partition_Join.
+End Partition_Join
*)
(*#*
inline "cic:/CoRN/ftc/Integral/integral_plus_integral.con".
(* UNEXPORTED
-End Integral_Sum.
+End Integral_Sum
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(*#*
include "ftc/PartFunEquality.ma".
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(*#* * Functions with compact domain
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/IntervalFunct/a.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/a.var" "Operations__".
-inline "cic:/CoRN/ftc/IntervalFunct/b.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/b.var" "Operations__".
-inline "cic:/CoRN/ftc/IntervalFunct/Hab.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/Hab.var" "Operations__".
(* begin hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/I.con".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/I.con" "Operations__".
(* end hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/f.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/f.var" "Operations__".
-inline "cic:/CoRN/ftc/IntervalFunct/g.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/g.var" "Operations__".
(* UNEXPORTED
-Section Const.
+Section Const
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/IntervalFunct/c.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/Const/c.var" "Operations__Const__".
inline "cic:/CoRN/ftc/IntervalFunct/IConst_strext.con".
inline "cic:/CoRN/ftc/IntervalFunct/IConst.con".
(* UNEXPORTED
-End Const.
+End Const
*)
inline "cic:/CoRN/ftc/IntervalFunct/IId_strext.con".
inline "cic:/CoRN/ftc/IntervalFunct/IMult.con".
(* UNEXPORTED
-Section Nth_Power.
+Section Nth_Power
*)
(*#*
Exponentiation to a natural power [n] is also useful.
*)
-inline "cic:/CoRN/ftc/IntervalFunct/n.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/Nth_Power/n.var" "Operations__Nth_Power__".
inline "cic:/CoRN/ftc/IntervalFunct/INth_strext.con".
inline "cic:/CoRN/ftc/IntervalFunct/INth.con".
(* UNEXPORTED
-End Nth_Power.
+End Nth_Power
*)
(*#*
*)
(* UNEXPORTED
-Section Recip_Div.
+Section Recip_Div
*)
(* begin show *)
-inline "cic:/CoRN/ftc/IntervalFunct/Hg.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Operations/Recip_Div/Hg.var" "Operations__Recip_Div__".
(* end show *)
inline "cic:/CoRN/ftc/IntervalFunct/IDiv.con".
(* UNEXPORTED
-End Recip_Div.
+End Recip_Div
*)
(*#*
inline "cic:/CoRN/ftc/IntervalFunct/IAbs.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(*#*
*)
(* UNEXPORTED
-Section Composition.
+Section Composition
*)
-inline "cic:/CoRN/ftc/IntervalFunct/a.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/a.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/b.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/b.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/Hab.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hab.var" "Composition__".
(* begin hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/I.con".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/I.con" "Composition__".
(* end hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/a'.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/a'.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/b'.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/b'.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/Hab'.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hab'.var" "Composition__".
(* begin hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/I'.con".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/I'.con" "Composition__".
(* end hide *)
-inline "cic:/CoRN/ftc/IntervalFunct/f.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/f.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/g.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/g.var" "Composition__".
-inline "cic:/CoRN/ftc/IntervalFunct/Hfg.var".
+inline "cic:/CoRN/ftc/IntervalFunct/Composition/Hfg.var" "Composition__".
inline "cic:/CoRN/ftc/IntervalFunct/IComp_strext.con".
inline "cic:/CoRN/ftc/IntervalFunct/IComp.con".
(* UNEXPORTED
-End Composition.
+End Composition
*)
(* UNEXPORTED
(*#* printing FSeries_Sum %\ensuremath{\sum_{\infty}}% #∑'<sub>∞</sub># *)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *More on Sequences and Series
but the ones which do we simply adapt in the usual way.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/J.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/f.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/F.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contf.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Definitions/contF.var" "Definitions__".
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_real_IR.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
*)
(*#*
Limit is defined and works in the same way as before.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/J.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/f.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/contf.var" "More_Definitions__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/conv.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Definitions/conv.var" "More_Definitions__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_fun_seq_Lim_char.con".
(* UNEXPORTED
-End More_Definitions.
+End More_Definitions
*)
(* UNEXPORTED
-Section Irrelevance_of_Proofs.
+Section Irrelevance_of_Proofs
*)
(*#* ***Basic Properties
Proofs are irrelevant as before---they just have to be present.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/J.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/f.var" "Irrelevance_of_Proofs__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contf0.var" "Irrelevance_of_Proofs__".
(* end show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/F.var" "Irrelevance_of_Proofs__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF.var" "Irrelevance_of_Proofs__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Irrelevance_of_Proofs/contF0.var" "Irrelevance_of_Proofs__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_seq_wd_IR.con".
(* UNEXPORTED
-End Irrelevance_of_Proofs.
+End Irrelevance_of_Proofs
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Properties.
+Section More_Properties
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/J.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/f.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/g.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contf0.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contg0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contg0.var" "More_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/Cauchy_conv_fun_seq'_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/F.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/G.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/G.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contF0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contF0.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contG.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contG0.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Properties/contG0.var" "More_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/conv_Cauchy_fun_seq_IR.con".
(* UNEXPORTED
-End More_Properties.
+End More_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Algebraic_Properties.
+Section Algebraic_Properties
*)
(*#* ***Algebraic Properties
Algebraic operations still work well.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/J.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/f.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/g.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contf.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contg.var" "Algebraic_Properties__".
inline "cic:/CoRN/ftc/MoreFunSeries/FLim_unique_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_const_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/F.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/F.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/G.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/G.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contF.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contG.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/contG.var" "Algebraic_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convF.var" "Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/convG.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Algebraic_Properties/convG.var" "Algebraic_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/fun_Lim_seq_mult'_IR.con".
(* UNEXPORTED
-End Algebraic_Properties.
+End Algebraic_Properties
*)
(* UNEXPORTED
-Section More_Algebraic_Properties.
+Section More_Algebraic_Properties
*)
(*#*
If we work with the limit function things fit in just as well.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/J.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/f.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/g.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contf.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contg.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/contg.var" "More_Algebraic_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/Hf.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hf.var" "More_Algebraic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunSeries/Hg.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Algebraic_Properties/Hg.var" "More_Algebraic_Properties__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunSeries/fun_Cauchy_prop_mult.con".
(* UNEXPORTED
-End More_Algebraic_Properties.
+End More_Algebraic_Properties
*)
(* UNEXPORTED
-Section Other.
+Section Other
*)
(*#* ***Miscellaneous
inline "cic:/CoRN/ftc/MoreFunSeries/fun_const_Lim.con".
(* UNEXPORTED
-End Other.
+End Other
*)
(* UNEXPORTED
-Section Series_Definitions.
+Section Series_Definitions
*)
(*#* **Series
Convergence is defined as expected---through convergence in every compact interval.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/J.var" "Series_Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/f.var" "Series_Definitions__".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_IR.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/H.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/H.var" "Series_Definitions__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/MoreFunSeries/h.con".
+inline "cic:/CoRN/ftc/MoreFunSeries/Series_Definitions/h.con" "Series_Definitions__".
(* end hide *)
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_char.con".
(* UNEXPORTED
-End Series_Definitions.
+End Series_Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Series_Definitions.
+Section More_Series_Definitions
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/J.var" "More_Series_Definitions__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/More_Series_Definitions/f.var" "More_Series_Definitions__".
(*#*
Absolute convergence still exists.
inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_abs_convergent_IR.con".
(* UNEXPORTED
-End More_Series_Definitions.
+End More_Series_Definitions
*)
(* UNEXPORTED
-Section Convergence_Results.
+Section Convergence_Results
*)
(*#*
As before, any series converges to its sum.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/J.var" "Convergence_Results__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Results/f.var" "Convergence_Results__".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_conv.con".
inline "cic:/CoRN/ftc/MoreFunSeries/Continuous_FSeries_Sum.con".
(* UNEXPORTED
-End Convergence_Results.
+End Convergence_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(*#* **Algebraic Operations
Convergence is well defined and preserved by operations.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/J.var" "Operations__".
inline "cic:/CoRN/ftc/MoreFunSeries/conv_fun_const_series_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_zero_IR.con".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/f.var" "Operations__".
-inline "cic:/CoRN/ftc/MoreFunSeries/g.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/g.var" "Operations__".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_series_convergent_wd_IR.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convF.var" "Operations__".
-inline "cic:/CoRN/ftc/MoreFunSeries/convG.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/convG.var" "Operations__".
(* end show *)
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/c.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/c.var" "Operations__".
-inline "cic:/CoRN/ftc/MoreFunSeries/H.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/H.var" "Operations__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contH.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Operations/contH.var" "Operations__".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal_conv.con".
inline "cic:/CoRN/ftc/MoreFunSeries/FSeries_Sum_scal.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(* UNEXPORTED
-Section Convergence_Criteria.
+Section Convergence_Criteria
*)
(*#* ***Convergence Criteria
comparison test (in both versions) and the ratio test.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/J.var" "Convergence_Criteria__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/f.var" "Convergence_Criteria__".
-inline "cic:/CoRN/ftc/MoreFunSeries/contF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Convergence_Criteria/contF.var" "Convergence_Criteria__".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_str_comparison_IR.con".
inline "cic:/CoRN/ftc/MoreFunSeries/fun_ratio_test_conv_IR.con".
(* UNEXPORTED
-End Convergence_Criteria.
+End Convergence_Criteria
*)
(* UNEXPORTED
-Section Insert_Series.
+Section Insert_Series
*)
(*#* ***Translation
position. This does not affect convergence or the sum of the series.
*)
-inline "cic:/CoRN/ftc/MoreFunSeries/J.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/J.var" "Insert_Series__".
-inline "cic:/CoRN/ftc/MoreFunSeries/f.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/f.var" "Insert_Series__".
-inline "cic:/CoRN/ftc/MoreFunSeries/convF.var".
+inline "cic:/CoRN/ftc/MoreFunSeries/Insert_Series/convF.var" "Insert_Series__".
inline "cic:/CoRN/ftc/MoreFunSeries/insert_series.con".
inline "cic:/CoRN/ftc/MoreFunSeries/insert_series_sum.con".
(* UNEXPORTED
-End Insert_Series.
+End Insert_Series
*)
*)
(* UNEXPORTED
-Section Basic_Results.
+Section Basic_Results
*)
(*#* *More about Functions
**Continuity
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/I.var" "Basic_Results__".
(*#*
Trivial stuff.
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/cI.var" "Basic_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/F.var" "Basic_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/contF.var" "Basic_Results__".
inline "cic:/CoRN/ftc/MoreFunctions/continuous_compact.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/Hinc.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Results/Hinc.var" "Basic_Results__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/FNorm_bnd_AbsIR.con".
(* UNEXPORTED
-End Basic_Results.
+End Basic_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Other_Results.
+Section Other_Results
*)
(*#*
The usual stuff.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/I.var" "Other_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/F.var" "Other_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/G.var" "Other_Results__".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_wd.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/contF.var" "Other_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Other_Results/contG.var" "Other_Results__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_recip.con".
(* UNEXPORTED
-End Other_Results.
+End Other_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/I.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/cI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/cI.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/F.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/G.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/contF.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/contG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Corollaries/contG.var" "Corollaries__".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_div.con".
inline "cic:/CoRN/ftc/MoreFunctions/FNorm_wd.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Sums.
+Section Sums
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Sums/I.var" "Sums__".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sumx.con".
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/f.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Sums/f.var" "Sums__".
-inline "cic:/CoRN/ftc/MoreFunctions/contF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Sums/contF.var" "Sums__".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum0.con".
inline "cic:/CoRN/ftc/MoreFunctions/Continuous_Sum.con".
(* UNEXPORTED
-End Sums.
+End Sums
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#* **Derivative
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/I.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/pI.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/F.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/G.var" "Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/H.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Basic_Properties/H.var" "Basic_Properties__".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_wdl.con".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_imp_Continuous'.con".
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_Results.
+Section More_Results
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/I.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/pI.var" "More_Results__".
(*#*
%\begin{convention}% Assume that [F'] and [G'] are derivatives of [F] and [G], respectively, in [I].
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/F.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/F'.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/G.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/G'.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/derF.var" "More_Results__".
-inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Results/derG.var" "More_Results__".
inline "cic:/CoRN/ftc/MoreFunctions/included_imp_Derivative.con".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_recip.con".
(* UNEXPORTED
-End More_Results.
+End More_Results
*)
(* UNEXPORTED
-Section More_Corollaries.
+Section More_Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/I.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/pI.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/F'.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/F'.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/G'.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/G'.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derF.var" "More_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/derG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/derG.var" "More_Corollaries__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/Gbnd.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Corollaries/Gbnd.var" "More_Corollaries__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_div.con".
(* UNEXPORTED
-End More_Corollaries.
+End More_Corollaries
*)
(* UNEXPORTED
-Section More_Sums.
+Section More_Sums
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/I.var" "More_Sums__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/pI.var" "More_Sums__".
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sumx.con".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/f.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/f.var" "More_Sums__".
-inline "cic:/CoRN/ftc/MoreFunctions/f'.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/f'.var" "More_Sums__".
-inline "cic:/CoRN/ftc/MoreFunctions/derF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/More_Sums/derF.var" "More_Sums__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_Sum.con".
(* UNEXPORTED
-End More_Sums.
+End More_Sums
*)
(* UNEXPORTED
-Section Diffble_Basic_Properties.
+Section Diffble_Basic_Properties
*)
(*#* **Differentiability
Mutatis mutandis for differentiability.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/I.var" "Diffble_Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/pI.var" "Diffble_Basic_Properties__".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_imp_inc.con".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_wd.con".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/F.var" "Diffble_Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/G.var" "Diffble_Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffF.var" "Diffble_Basic_Properties__".
-inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Basic_Properties/diffG.var" "Diffble_Basic_Properties__".
(*#*
%\begin{convention}% Assume [F] and [G] are differentiable in [I].
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_recip.con".
(* UNEXPORTED
-End Diffble_Basic_Properties.
+End Diffble_Basic_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Diffble_Corollaries.
+Section Diffble_Corollaries
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/I.var" "Diffble_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/pI.var" "Diffble_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/F.var" "Diffble_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/G.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/G.var" "Diffble_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffF.var" "Diffble_Corollaries__".
-inline "cic:/CoRN/ftc/MoreFunctions/diffG.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Corollaries/diffG.var" "Diffble_Corollaries__".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_div.con".
inline "cic:/CoRN/ftc/MoreFunctions/Diffble_Sum.con".
(* UNEXPORTED
-End Diffble_Corollaries.
+End Diffble_Corollaries
*)
(* UNEXPORTED
-Section Nth_Derivative.
+Section Nth_Derivative
*)
(*#* **Nth Derivative
Higher order derivatives pose more interesting problems. It turns out that it really becomes necessary to generalize our [n_deriv] operator to any interval.
*)
-inline "cic:/CoRN/ftc/MoreFunctions/I.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/I.var" "Nth_Derivative__".
-inline "cic:/CoRN/ftc/MoreFunctions/pI.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/pI.var" "Nth_Derivative__".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreFunctions/n.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/n.var" "Nth_Derivative__Definitions__".
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/F.var" "Nth_Derivative__Definitions__".
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Definitions/diffF.var" "Nth_Derivative__Definitions__".
inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv_fun.con".
inline "cic:/CoRN/ftc/MoreFunctions/N_Deriv.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section Basic_Results.
+Section Basic_Results
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_plus.con".
(* UNEXPORTED
-End Basic_Results.
+End Basic_Results
*)
(* UNEXPORTED
-Section More_Results.
+Section More_Results
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_Sn.con".
(* UNEXPORTED
-End More_Results.
+End More_Results
*)
(* UNEXPORTED
-Section Derivating_Diffble.
+Section Derivating_Diffble
*)
(*#*
As a special case we get a differentiation operator%\ldots%#...#
*)
-inline "cic:/CoRN/ftc/MoreFunctions/F.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/F.var" "Nth_Derivative__Derivating_Diffble__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreFunctions/diffF.var".
+inline "cic:/CoRN/ftc/MoreFunctions/Nth_Derivative/Derivating_Diffble/diffF.var" "Nth_Derivative__Derivating_Diffble__".
(* end show *)
inline "cic:/CoRN/ftc/MoreFunctions/Deriv.con".
(* UNEXPORTED
-End Derivating_Diffble.
+End Derivating_Diffble
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
(*#*
inline "cic:/CoRN/ftc/MoreFunctions/Derivative_n_imp_Continuous'.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
(* UNEXPORTED
-End Nth_Derivative.
+End Nth_Derivative
*)
(* UNEXPORTED
include "ftc/MoreFunctions.ma".
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* printing Integral %\ensuremath{\int}% #∫# *)
Before we define the new integral we need to some trivial interval inclusions.
*)
-inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/a.var" "Lemmas__".
-inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/b.var" "Lemmas__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Lemmas/Hab.var" "Lemmas__".
inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_lft.con".
inline "cic:/CoRN/ftc/MoreIntegrals/compact_inc_Min_rht.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#*
[<=] b].
*)
-inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/b.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/Hab.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/F.var" "Definitions__".
-inline "cic:/CoRN/ftc/MoreIntegrals/HF.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Definitions/HF.var" "Definitions__".
inline "cic:/CoRN/ftc/MoreIntegrals/Integral_inc1.con".
inline "cic:/CoRN/ftc/MoreIntegrals/Integral_integral.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Properties_of_Integral.
+Section Properties_of_Integral
*)
(*#* **Properties of the Integral
new ones, too. We begin with (strong) extensionality.
*)
-inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/a.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/b.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/Hab.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/F.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/G.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/G.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/contF.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contF.var" "Properties_of_Integral__".
-inline "cic:/CoRN/ftc/MoreIntegrals/contG.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Properties_of_Integral/contG.var" "Properties_of_Integral__".
inline "cic:/CoRN/ftc/MoreIntegrals/Integral_strext.con".
inline "cic:/CoRN/ftc/MoreIntegrals/Integral_leEq_norm.con".
(* UNEXPORTED
-End Properties_of_Integral.
+End Properties_of_Integral
*)
(* UNEXPORTED
-Section More_Properties.
+Section More_Properties
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/a.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/b.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/c.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/c.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab'.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab'.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hac'.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac'.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hcb'.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb'.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc'.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc'.var" "More_Properties__".
(* end show *)
-inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/F.var" "More_Properties__".
(* begin show *)
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hab.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hac.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hac.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hcb.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Hcb.var" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc.var" "More_Properties__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ab.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ab.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_ac.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_ac.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_cb.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_cb.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_a.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_a.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_b.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_b.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_abc_c.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_abc_c.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_a.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_a.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_c.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_c.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_a.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_a.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_ab_b.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ab_b.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_cb_b.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_cb_b.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/le_ac_c.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/le_ac_c.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_abc.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_abc.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ab.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ab.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_ac.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_ac.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_cb.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_cb.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_a.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_a.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_b.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_b.con" "More_Properties__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Habc_c.con".
+inline "cic:/CoRN/ftc/MoreIntegrals/More_Properties/Habc_c.con" "More_Properties__".
(* end hide *)
*)
(* UNEXPORTED
-End More_Properties.
+End More_Properties
*)
(* UNEXPORTED
-Section Corollaries.
+Section Corollaries
*)
-inline "cic:/CoRN/ftc/MoreIntegrals/a.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/a.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreIntegrals/b.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/b.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreIntegrals/Hab.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/Hab.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreIntegrals/F.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/F.var" "Corollaries__".
-inline "cic:/CoRN/ftc/MoreIntegrals/contF.var".
+inline "cic:/CoRN/ftc/MoreIntegrals/Corollaries/contF.var" "Corollaries__".
(*#* As a corollary, we get the following rule: *)
inline "cic:/CoRN/ftc/MoreIntegrals/ub_Integral.con".
(* UNEXPORTED
-End Corollaries.
+End Corollaries
*)
inline "cic:/CoRN/ftc/MoreIntegrals/Integral_ap_zero.con".
*)
(* UNEXPORTED
-Section Intervals.
+Section Intervals
*)
(*#* printing realline %\ensuremath{\RR}% #(-∞,+∞)# *)
inline "cic:/CoRN/ftc/MoreIntervals/iprop_wd.con".
(* UNEXPORTED
-End Intervals.
+End Intervals
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Compact_Constructions.
+Section Compact_Constructions
*)
(* UNEXPORTED
-Section Single_Compact_Interval.
+Section Single_Compact_Interval
*)
(*#* **Constructions with Compact Intervals
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreIntervals/P.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/P.var" "Compact_Constructions__Single_Compact_Interval__".
-inline "cic:/CoRN/ftc/MoreIntervals/wdP.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/wdP.var" "Compact_Constructions__Single_Compact_Interval__".
-inline "cic:/CoRN/ftc/MoreIntervals/x.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/x.var" "Compact_Constructions__Single_Compact_Interval__".
-inline "cic:/CoRN/ftc/MoreIntervals/Hx.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Single_Compact_Interval/Hx.var" "Compact_Constructions__Single_Compact_Interval__".
inline "cic:/CoRN/ftc/MoreIntervals/compact_single.con".
inline "cic:/CoRN/ftc/MoreIntervals/compact_single_inc.con".
(* UNEXPORTED
-End Single_Compact_Interval.
+End Single_Compact_Interval
*)
(*#*
*)
(* UNEXPORTED
-Section Proper_Compact_with_One_or_Two_Points.
+Section Proper_Compact_with_One_or_Two_Points
*)
(* begin hide *)
-inline "cic:/CoRN/ftc/MoreIntervals/cip1'.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip1''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip1'''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip1''''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip1''''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip2.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip2'.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip2''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip2'''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip2'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip3.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip3'.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip3''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
-inline "cic:/CoRN/ftc/MoreIntervals/cip3'''.con".
+inline "cic:/CoRN/ftc/MoreIntervals/Compact_Constructions/Proper_Compact_with_One_or_Two_Points/cip3'''.con" "Compact_Constructions__Proper_Compact_with_One_or_Two_Points__".
(* end hide *)
inline "cic:/CoRN/ftc/MoreIntervals/compact_in_interval_y_rht.con".
(* UNEXPORTED
-End Proper_Compact_with_One_or_Two_Points.
+End Proper_Compact_with_One_or_Two_Points
*)
(*#*
inline "cic:/CoRN/ftc/MoreIntervals/compact_proper_in_interval.con".
(* UNEXPORTED
-End Compact_Constructions.
+End Compact_Constructions
*)
(* UNEXPORTED
-Section Functions.
+Section Functions
*)
(*#* **Properties of Functions in Intervals
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/MoreIntervals/n.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Functions/n.var" "Functions__".
-inline "cic:/CoRN/ftc/MoreIntervals/I.var".
+inline "cic:/CoRN/ftc/MoreIntervals/Functions/I.var" "Functions__".
inline "cic:/CoRN/ftc/MoreIntervals/Continuous.con".
inline "cic:/CoRN/ftc/MoreIntervals/Diffble_n.con".
(* UNEXPORTED
-End Functions.
+End Functions
*)
(* UNEXPORTED
-Section Reflexivity_Properties.
+Section Reflexivity_Properties
*)
(*#*
inline "cic:/CoRN/ftc/MoreIntervals/Int_Diffble.con".
(* UNEXPORTED
-End Reflexivity_Properties.
+End Reflexivity_Properties
*)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#*
inline "cic:/CoRN/ftc/MoreIntervals/included_Feq'.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
include "ftc/Differentiability.ma".
(* UNEXPORTED
-Section Nth_Derivative.
+Section Nth_Derivative
*)
(*#* *Nth Derivative
We first define what we mean by the derivative of order [n] of a function.
*)
-inline "cic:/CoRN/ftc/NthDerivative/a.var".
+inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/a.var" "Nth_Derivative__".
-inline "cic:/CoRN/ftc/NthDerivative/b.var".
+inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/b.var" "Nth_Derivative__".
-inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
+inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab'.var" "Nth_Derivative__".
(* begin hide *)
-inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
+inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/Hab.con" "Nth_Derivative__".
-inline "cic:/CoRN/ftc/NthDerivative/I.con".
+inline "cic:/CoRN/ftc/NthDerivative/Nth_Derivative/I.con" "Nth_Derivative__".
(* end hide *)
inline "cic:/CoRN/ftc/NthDerivative/Diffble_I_n.con".
(* UNEXPORTED
-End Nth_Derivative.
+End Nth_Derivative
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Trivia.
+Section Trivia
*)
(*#* **Trivia
These are the expected extensionality and uniqueness results.
*)
-inline "cic:/CoRN/ftc/NthDerivative/a.var".
+inline "cic:/CoRN/ftc/NthDerivative/Trivia/a.var" "Trivia__".
-inline "cic:/CoRN/ftc/NthDerivative/b.var".
+inline "cic:/CoRN/ftc/NthDerivative/Trivia/b.var" "Trivia__".
-inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
+inline "cic:/CoRN/ftc/NthDerivative/Trivia/Hab'.var" "Trivia__".
(* begin hide *)
-inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
+inline "cic:/CoRN/ftc/NthDerivative/Trivia/Hab.con" "Trivia__".
-inline "cic:/CoRN/ftc/NthDerivative/I.con".
+inline "cic:/CoRN/ftc/NthDerivative/Trivia/I.con" "Trivia__".
(* end hide *)
inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_unique.con".
(* UNEXPORTED
-End Trivia.
+End Trivia
*)
(* UNEXPORTED
-Section Basic_Results.
+Section Basic_Results
*)
(*#* **Basic Results
definition of [Diffble_I_n].
*)
-inline "cic:/CoRN/ftc/NthDerivative/a.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/a.var" "Basic_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/b.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/b.var" "Basic_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab'.var" "Basic_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/Hab.con" "Basic_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/I.con".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/I.con" "Basic_Results__".
(* end hide *)
inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_imp_inc'.con".
(* UNEXPORTED
-Section aux.
+Section aux
*)
(*#*
(* begin show *)
-inline "cic:/CoRN/ftc/NthDerivative/F.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/F.var" "Basic_Results__aux__".
-inline "cic:/CoRN/ftc/NthDerivative/diffF.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffF.var" "Basic_Results__aux__".
-inline "cic:/CoRN/ftc/NthDerivative/diffFn.var".
+inline "cic:/CoRN/ftc/NthDerivative/Basic_Results/aux/diffFn.var" "Basic_Results__aux__".
(* end show *)
inline "cic:/CoRN/ftc/NthDerivative/deriv_1_deriv'.con".
(* UNEXPORTED
-End aux.
+End aux
*)
(*#*
inline "cic:/CoRN/ftc/NthDerivative/Derivative_I_n_plus.con".
(* UNEXPORTED
-End Basic_Results.
+End Basic_Results
*)
(* UNEXPORTED
-Section More_Results.
+Section More_Results
*)
-inline "cic:/CoRN/ftc/NthDerivative/a.var".
+inline "cic:/CoRN/ftc/NthDerivative/More_Results/a.var" "More_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/b.var".
+inline "cic:/CoRN/ftc/NthDerivative/More_Results/b.var" "More_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/Hab'.var".
+inline "cic:/CoRN/ftc/NthDerivative/More_Results/Hab'.var" "More_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/NthDerivative/Hab.con".
+inline "cic:/CoRN/ftc/NthDerivative/More_Results/Hab.con" "More_Results__".
-inline "cic:/CoRN/ftc/NthDerivative/I.con".
+inline "cic:/CoRN/ftc/NthDerivative/More_Results/I.con" "More_Results__".
(* end hide *)
inline "cic:/CoRN/ftc/NthDerivative/n_deriv_plus.con".
(* UNEXPORTED
-End More_Results.
+End More_Results
*)
(* UNEXPORTED
-Section More_on_n_deriv.
+Section More_on_n_deriv
*)
(*#*
inline "cic:/CoRN/ftc/NthDerivative/n_deriv_I_strext'.con".
(* UNEXPORTED
-End More_on_n_deriv.
+End More_on_n_deriv
*)
include "tactics/DiffTactics1.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Equality of Partial Functions
*)
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section Equality_Results.
+Section Equality_Results
*)
(*#* **Properties of Inclusion
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/I.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/I.var" "Equality_Results__".
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/F.var" "Equality_Results__".
-inline "cic:/CoRN/ftc/PartFunEquality/G.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/G.var" "Equality_Results__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/P.con".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/P.con" "Equality_Results__".
-inline "cic:/CoRN/ftc/PartFunEquality/Q.con".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/Q.con" "Equality_Results__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/R.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Equality_Results/R.var" "Equality_Results__".
(*#*
We start with two lemmas which make it much easier to prove and use
inline "cic:/CoRN/ftc/PartFunEquality/included_IR.con".
(* UNEXPORTED
-End Equality_Results.
+End Equality_Results
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Some_More.
+Section Some_More
*)
(*#*
inline "cic:/CoRN/ftc/PartFunEquality/included_Feq.con".
(* UNEXPORTED
-End Some_More.
+End Some_More
*)
(* UNEXPORTED
-Section Away_from_Zero.
+Section Away_from_Zero
*)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* **Away from Zero
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/I.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/I.var" "Away_from_Zero__Definitions__".
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/F.var" "Away_from_Zero__Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/P.con".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/P.con" "Away_from_Zero__Definitions__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/PartFunEquality/Hf.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Definitions/Hf.var" "Away_from_Zero__Definitions__".
(* end show *)
inline "cic:/CoRN/ftc/PartFunEquality/bnd_imp_inc_div.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/F.var" "Away_from_Zero__".
-inline "cic:/CoRN/ftc/PartFunEquality/P.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/P.var" "Away_from_Zero__".
-inline "cic:/CoRN/ftc/PartFunEquality/Q.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Away_from_Zero/Q.var" "Away_from_Zero__".
inline "cic:/CoRN/ftc/PartFunEquality/included_imp_bnd.con".
inline "cic:/CoRN/ftc/PartFunEquality/FRestr_bnd'.con".
(* UNEXPORTED
-End Away_from_Zero.
+End Away_from_Zero
*)
(* UNEXPORTED
(* end hide *)
(* UNEXPORTED
-Section More_on_Equality.
+Section More_on_Equality
*)
(*#* **Properties of Equality
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/I.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/I.var" "More_on_Equality__".
(* UNEXPORTED
-Section Feq_Equivalence.
+Section Feq_Equivalence
*)
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/F.var" "More_on_Equality__Feq_Equivalence__".
-inline "cic:/CoRN/ftc/PartFunEquality/G.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/G.var" "More_on_Equality__Feq_Equivalence__".
-inline "cic:/CoRN/ftc/PartFunEquality/H.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Feq_Equivalence/H.var" "More_on_Equality__Feq_Equivalence__".
inline "cic:/CoRN/ftc/PartFunEquality/Feq_reflexive.con".
inline "cic:/CoRN/ftc/PartFunEquality/Feq_transitive.con".
(* UNEXPORTED
-End Feq_Equivalence.
+End Feq_Equivalence
*)
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(*#*
Also it is preserved through application of functional constructors and restriction.
*)
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F.var" "More_on_Equality__Operations__".
-inline "cic:/CoRN/ftc/PartFunEquality/F'.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/F'.var" "More_on_Equality__Operations__".
-inline "cic:/CoRN/ftc/PartFunEquality/G.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G.var" "More_on_Equality__Operations__".
-inline "cic:/CoRN/ftc/PartFunEquality/G'.var".
+inline "cic:/CoRN/ftc/PartFunEquality/More_on_Equality/Operations/G'.var" "More_on_Equality__Operations__".
inline "cic:/CoRN/ftc/PartFunEquality/Feq_plus.con".
inline "cic:/CoRN/ftc/PartFunEquality/fun_image_wd.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(* UNEXPORTED
-End More_on_Equality.
+End More_on_Equality
*)
(* UNEXPORTED
-Section Nth_Power.
+Section Nth_Power
*)
(*#* **Nth Power
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/F.var" "Nth_Power__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/P.con".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/P.con" "Nth_Power__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/Q.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Q.var" "Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/H.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H.var" "Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/Hf.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/Hf.var" "Nth_Power__".
inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero.con".
-inline "cic:/CoRN/ftc/PartFunEquality/n.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/n.var" "Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/H'.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Nth_Power/H'.var" "Nth_Power__".
inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult.con".
(* UNEXPORTED
-End Nth_Power.
+End Nth_Power
*)
(* UNEXPORTED
-Section Strong_Nth_Power.
+Section Strong_Nth_Power
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartFunEquality/a.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/a.var" "Strong_Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/b.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/b.var" "Strong_Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/Hab.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/Hab.var" "Strong_Nth_Power__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/I.con".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/I.con" "Strong_Nth_Power__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartFunEquality/F.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/F.var" "Strong_Nth_Power__".
-inline "cic:/CoRN/ftc/PartFunEquality/incF.var".
+inline "cic:/CoRN/ftc/PartFunEquality/Strong_Nth_Power/incF.var" "Strong_Nth_Power__".
inline "cic:/CoRN/ftc/PartFunEquality/FNth_zero'.con".
inline "cic:/CoRN/ftc/PartFunEquality/FNth_mult'.con".
(* UNEXPORTED
-End Strong_Nth_Power.
+End Strong_Nth_Power
*)
include "ftc/IntervalFunct.ma".
(* UNEXPORTED
-Section Conversion.
+Section Conversion
*)
(*#* *Correspondence
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartInterval/F.var".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/F.var" "Conversion__".
-inline "cic:/CoRN/ftc/PartInterval/a.var".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/a.var" "Conversion__".
-inline "cic:/CoRN/ftc/PartInterval/b.var".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/b.var" "Conversion__".
-inline "cic:/CoRN/ftc/PartInterval/Hab.var".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/Hab.var" "Conversion__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartInterval/I.con".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/I.con" "Conversion__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartInterval/Hf.var".
+inline "cic:/CoRN/ftc/PartInterval/Conversion/Hf.var" "Conversion__".
inline "cic:/CoRN/ftc/PartInterval/IntPartIR_strext.con".
inline "cic:/CoRN/ftc/PartInterval/IntPartIR.con".
(* UNEXPORTED
-End Conversion.
+End Conversion
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section AntiConversion.
+Section AntiConversion
*)
(*#*
domain [[a,b]] and build the corresponding partial function.
*)
-inline "cic:/CoRN/ftc/PartInterval/a.var".
+inline "cic:/CoRN/ftc/PartInterval/AntiConversion/a.var" "AntiConversion__".
-inline "cic:/CoRN/ftc/PartInterval/b.var".
+inline "cic:/CoRN/ftc/PartInterval/AntiConversion/b.var" "AntiConversion__".
-inline "cic:/CoRN/ftc/PartInterval/Hab.var".
+inline "cic:/CoRN/ftc/PartInterval/AntiConversion/Hab.var" "AntiConversion__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartInterval/I.con".
+inline "cic:/CoRN/ftc/PartInterval/AntiConversion/I.con" "AntiConversion__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartInterval/f.var".
+inline "cic:/CoRN/ftc/PartInterval/AntiConversion/f.var" "AntiConversion__".
inline "cic:/CoRN/ftc/PartInterval/PartInt_strext.con".
inline "cic:/CoRN/ftc/PartInterval/PartInt.con".
(* UNEXPORTED
-End AntiConversion.
+End AntiConversion
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Inverses.
+Section Inverses
*)
(*#*
inline "cic:/CoRN/ftc/PartInterval/int_part_int.con".
(* UNEXPORTED
-End Inverses.
+End Inverses
*)
(* UNEXPORTED
-Section Equivalences.
+Section Equivalences
*)
(*#* **Mappings Preserve Operations
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/PartInterval/F.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/F.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/G.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/G.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/a.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/a.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/b.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/b.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/c.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/c.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/Hab.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/Hab.var" "Equivalences__".
(* begin hide *)
-inline "cic:/CoRN/ftc/PartInterval/I.con".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/I.con" "Equivalences__".
(* end hide *)
-inline "cic:/CoRN/ftc/PartInterval/f.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/f.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/g.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/g.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/Ff.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/Ff.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/Gg.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/Gg.var" "Equivalences__".
inline "cic:/CoRN/ftc/PartInterval/part_int_const.con".
(* begin show *)
-inline "cic:/CoRN/ftc/PartInterval/HG.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/HG.var" "Equivalences__".
-inline "cic:/CoRN/ftc/PartInterval/Hg.var".
+inline "cic:/CoRN/ftc/PartInterval/Equivalences/Hg.var" "Equivalences__".
(* end show *)
inline "cic:/CoRN/ftc/PartInterval/part_int_div.con".
(* UNEXPORTED
-End Equivalences.
+End Equivalences
*)
(*#* printing Partition_Sum %\ensuremath{\sum_P}% #∑<sub>P</sub># *)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Partitions
inline "cic:/CoRN/ftc/Partitions/Even_Partition.con".
(* UNEXPORTED
-Section Refinements.
+Section Refinements
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/a.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/b.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Hab.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/m.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/m.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/n.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/n.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/P.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/P.var" "Definitions__Refinements__".
-inline "cic:/CoRN/ftc/Partitions/Q.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Refinements/Q.var" "Definitions__Refinements__".
(*#*
We now define what it means for a partition [Q] to be a refinement of
inline "cic:/CoRN/ftc/Partitions/Partition_Sum.con".
(* UNEXPORTED
-End Refinements.
+End Refinements
*)
(* UNEXPORTED
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/b.var" "Definitions__".
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Hab.var" "Definitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Partitions/I.con".
+inline "cic:/CoRN/ftc/Partitions/Definitions/I.con" "Definitions__".
(* end hide *)
(* UNEXPORTED
-Section Getting_Points.
+Section Getting_Points
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Partitions/m.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/m.var" "Definitions__Getting_Points__".
-inline "cic:/CoRN/ftc/Partitions/Q.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/Getting_Points/Q.var" "Definitions__Getting_Points__".
inline "cic:/CoRN/ftc/Partitions/Partition_imp_points.con".
inline "cic:/CoRN/ftc/Partitions/Partition_imp_points_2.con".
(* UNEXPORTED
-End Getting_Points.
+End Getting_Points
*)
(*#*
As a corollary, given any continuous function [F] and a natural number we have an immediate choice of a sum of [F] in [[a,b]].
*)
-inline "cic:/CoRN/ftc/Partitions/F.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/F.var" "Definitions__".
-inline "cic:/CoRN/ftc/Partitions/contF.var".
+inline "cic:/CoRN/ftc/Partitions/Definitions/contF.var" "Definitions__".
inline "cic:/CoRN/ftc/Partitions/Even_Partition_Sum.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* ** Properties of the mesh
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/a.var" "Lemmas__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/b.var" "Lemmas__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Partitions/I.con".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/I.con" "Lemmas__".
(* end hide *)
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/Hab.var" "Lemmas__".
-inline "cic:/CoRN/ftc/Partitions/n.var".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/n.var" "Lemmas__".
-inline "cic:/CoRN/ftc/Partitions/P.var".
+inline "cic:/CoRN/ftc/Partitions/Lemmas/P.var" "Lemmas__".
inline "cic:/CoRN/ftc/Partitions/Mesh_lemma.con".
inline "cic:/CoRN/ftc/Partitions/Mesh_leEq.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section Even_Partitions.
+Section Even_Partitions
*)
(*#* More technical stuff. Two equal partitions have the same mesh.
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/a.var" "Even_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/b.var" "Even_Partitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Partitions/I.con".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/I.con" "Even_Partitions__".
(* end hide *)
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hab.var" "Even_Partitions__".
(*#*
An interesting property: in a partition, if [ai [<] aj] then [i < j].
Even partitions always have a common refinement.
*)
-inline "cic:/CoRN/ftc/Partitions/m.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/m.var" "Even_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/n.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/n.var" "Even_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/Hm.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hm.var" "Even_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/Hn.var".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Hn.var" "Even_Partitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Partitions/P.con".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/P.con" "Even_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/Q.con".
+inline "cic:/CoRN/ftc/Partitions/Even_Partitions/Q.con" "Even_Partitions__".
(* end hide *)
inline "cic:/CoRN/ftc/Partitions/even_partition_refinement.con".
(* UNEXPORTED
-End Even_Partitions.
+End Even_Partitions
*)
(* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
*)
(*#* ** Separation
Some auxiliary definitions. A partition is said to be separated if all its points are distinct.
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/a.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/b.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/Hab.var" "More_Definitions__".
inline "cic:/CoRN/ftc/Partitions/_Separated.con".
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Partitions/n.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/n.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/Partitions/m.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/m.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/Partitions/P.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/P.var" "More_Definitions__".
-inline "cic:/CoRN/ftc/Partitions/Q.var".
+inline "cic:/CoRN/ftc/Partitions/More_Definitions/Q.var" "More_Definitions__".
inline "cic:/CoRN/ftc/Partitions/Separated.con".
(* UNEXPORTED
-End More_Definitions.
+End More_Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Sep_Partitions.
+Section Sep_Partitions
*)
-inline "cic:/CoRN/ftc/Partitions/a.var".
+inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/a.var" "Sep_Partitions__".
-inline "cic:/CoRN/ftc/Partitions/b.var".
+inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/b.var" "Sep_Partitions__".
(* begin hide *)
-inline "cic:/CoRN/ftc/Partitions/I.con".
+inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/I.con" "Sep_Partitions__".
(* end hide *)
-inline "cic:/CoRN/ftc/Partitions/Hab.var".
+inline "cic:/CoRN/ftc/Partitions/Sep_Partitions/Hab.var" "Sep_Partitions__".
(*#*
The antimesh of a separated partition is always positive.
inline "cic:/CoRN/ftc/Partitions/partition_less_imp_gt_zero.con".
(* UNEXPORTED
-End Sep_Partitions.
+End Sep_Partitions
*)
include "ftc/RefSepRef.ma".
(* UNEXPORTED
-Section Refinement_Lemma.
+Section Refinement_Lemma
*)
(*#* *The Refinement Lemmas
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/RefLemma/a.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/a.var" "Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/b.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/b.var" "Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Hab.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Hab.var" "Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/I.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/I.con" "Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/F.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/F.var" "Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/contF.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF.var" "Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/incF.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/incF.var" "Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/contF'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/contF'.con" "Refinement_Lemma__".
(* end hide *)
(* UNEXPORTED
-Section First_Refinement_Lemma.
+Section First_Refinement_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/RefLemma/e.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/e.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/He.var" "Refinement_Lemma__First_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/d.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/d.con" "Refinement_Lemma__First_Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/m.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/m.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/n.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/n.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/P.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/P.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HMesh.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HMesh.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Q.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Q.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Href.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/Href.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fP.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfP'.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fQ.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/fQ.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfQ.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ.var" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfQ'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/HfQ'.var" "Refinement_Lemma__First_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/sub.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/sub.con" "Refinement_Lemma__First_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_sub_0.con".
inline "cic:/CoRN/ftc/RefLemma/RL_sub_S.con".
-inline "cic:/CoRN/ftc/RefLemma/H.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H.con" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/H'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H'.con" "Refinement_Lemma__First_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/H0.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/First_Refinement_Lemma/H0.con" "Refinement_Lemma__First_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_sub_SS.con".
inline "cic:/CoRN/ftc/RefLemma/first_refinement_lemma.con".
(* UNEXPORTED
-End First_Refinement_Lemma.
+End First_Refinement_Lemma
*)
(* UNEXPORTED
-Section Second_Refinement_Lemma.
+Section Second_Refinement_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/RefLemma/n.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/n.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/j.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/j.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/k.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/k.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/P.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/P.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Q.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/Q.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/R.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/R.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HrefP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefP.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HrefR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HrefR.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/e'.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/He'.var" "Refinement_Lemma__Second_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/d.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d.con" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/d'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/d'.con" "Refinement_Lemma__Second_Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fP.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/fR.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR.var" "Refinement_Lemma__Second_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Second_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Second_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/second_refinement_lemma.con".
(* UNEXPORTED
-End Second_Refinement_Lemma.
+End Second_Refinement_Lemma
*)
(* UNEXPORTED
-Section Third_Refinement_Lemma.
+Section Third_Refinement_Lemma
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/RefLemma/n.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/n.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/m.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/m.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/P.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/R.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/e'.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/He'.var" "Refinement_Lemma__Third_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/d.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d.con" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/d'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/d'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Hab'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hab'.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/beta.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/beta.var" "Refinement_Lemma__Third_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/Hbeta.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Hbeta.var" "Refinement_Lemma__Third_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/alpha.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/alpha.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_alpha.con".
-inline "cic:/CoRN/ftc/RefLemma/csi1.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi1.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_csi1.con".
-inline "cic:/CoRN/ftc/RefLemma/delta1.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta1.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_delta1.con".
-inline "cic:/CoRN/ftc/RefLemma/P'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/P'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_P'_sep.con".
inline "cic:/CoRN/ftc/RefLemma/RL_P'_Mesh.con".
-inline "cic:/CoRN/ftc/RefLemma/fP'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fP'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_fP'_in_P'.con".
inline "cic:/CoRN/ftc/RefLemma/RL_P'_P_sum.con".
-inline "cic:/CoRN/ftc/RefLemma/csi2.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi2.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_csi2.con".
-inline "cic:/CoRN/ftc/RefLemma/delta2.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/delta2.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_delta2.con".
-inline "cic:/CoRN/ftc/RefLemma/R'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/R'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_R'_sep.con".
inline "cic:/CoRN/ftc/RefLemma/RL_R'_Mesh.con".
-inline "cic:/CoRN/ftc/RefLemma/fR'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fR'.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_fR'_in_R'.con".
inline "cic:/CoRN/ftc/RefLemma/RL_R'_R_sum.con".
-inline "cic:/CoRN/ftc/RefLemma/csi3.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/csi3.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_csi3.con".
-inline "cic:/CoRN/ftc/RefLemma/Q.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/Q.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_Q_Mesh.con".
inline "cic:/CoRN/ftc/RefLemma/RL_Q_sep.con".
-inline "cic:/CoRN/ftc/RefLemma/fQ.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Third_Refinement_Lemma/fQ.con" "Refinement_Lemma__Third_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/RL_fQ_in_Q.con".
inline "cic:/CoRN/ftc/RefLemma/third_refinement_lemma.con".
(* UNEXPORTED
-End Third_Refinement_Lemma.
+End Third_Refinement_Lemma
*)
(* UNEXPORTED
-Section Fourth_Refinement_Lemma.
+Section Fourth_Refinement_Lemma
*)
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/Fa.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Fa.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
(* NOTATION
Notation just := (fun z => incF _ (Pts_part_lemma _ _ _ _ _ _ z _ _)).
above)
*)
-inline "cic:/CoRN/ftc/RefLemma/n.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/n.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/m.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/m.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/P.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/P.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/R.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/R.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/e'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/He'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/d.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/d'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/d'.con" "Refinement_Lemma__Fourth_Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/fR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
(* begin show *)
-inline "cic:/CoRN/ftc/RefLemma/Hab'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Fourth_Refinement_Lemma/Hab'.var" "Refinement_Lemma__Fourth_Refinement_Lemma__".
(* end show *)
inline "cic:/CoRN/ftc/RefLemma/fourth_refinement_lemma.con".
(* UNEXPORTED
-End Fourth_Refinement_Lemma.
+End Fourth_Refinement_Lemma
*)
(* UNEXPORTED
-Section Main_Refinement_Lemma.
+Section Main_Refinement_Lemma
*)
(*#* We finish by presenting Theorem 9. *)
-inline "cic:/CoRN/ftc/RefLemma/n.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/n.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/m.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/m.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/P.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/P.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/R.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/R.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/e'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/e'.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/He'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/He'.var" "Refinement_Lemma__Main_Refinement_Lemma__".
(* begin hide *)
-inline "cic:/CoRN/ftc/RefLemma/d.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d.con" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/d'.con".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/d'.con" "Refinement_Lemma__Main_Refinement_Lemma__".
(* end hide *)
-inline "cic:/CoRN/ftc/RefLemma/HMeshP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshP.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HMeshR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HMeshR.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fP.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfP'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfP'.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/fR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/fR.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR.var" "Refinement_Lemma__Main_Refinement_Lemma__".
-inline "cic:/CoRN/ftc/RefLemma/HfR'.var".
+inline "cic:/CoRN/ftc/RefLemma/Refinement_Lemma/Main_Refinement_Lemma/HfR'.var" "Refinement_Lemma__Main_Refinement_Lemma__".
inline "cic:/CoRN/ftc/RefLemma/refinement_lemma.con".
(* UNEXPORTED
-End Main_Refinement_Lemma.
+End Main_Refinement_Lemma
*)
(* UNEXPORTED
-End Refinement_Lemma.
+End Refinement_Lemma
*)
include "ftc/Partitions.ma".
(* UNEXPORTED
-Section Refining_Separated.
+Section Refining_Separated
*)
-inline "cic:/CoRN/ftc/RefSepRef/a.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/a.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/b.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/b.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/Hab.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/Hab.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/I.con".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/I.con" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/F.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/F.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/contF.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/contF.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/incF.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/incF.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/m.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/m.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/n.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/n.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/P.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/P.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/R.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/R.var" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/HPR.var".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/HPR.var" "Refining_Separated__".
inline "cic:/CoRN/ftc/RefSepRef/RSR_HP.con".
inline "cic:/CoRN/ftc/RefSepRef/RSR_H'.con".
-inline "cic:/CoRN/ftc/RefSepRef/f'.con".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/f'.con" "Refining_Separated__".
-inline "cic:/CoRN/ftc/RefSepRef/g'.con".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/g'.con" "Refining_Separated__".
inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_nlnf.con".
inline "cic:/CoRN/ftc/RefSepRef/RSR_f'_ap_g'.con".
-inline "cic:/CoRN/ftc/RefSepRef/h.con".
+inline "cic:/CoRN/ftc/RefSepRef/Refining_Separated/h.con" "Refining_Separated__".
inline "cic:/CoRN/ftc/RefSepRef/RSR_h_nlnf.con".
inline "cic:/CoRN/ftc/RefSepRef/Separated_Refinement_rht.con".
(* UNEXPORTED
-End Refining_Separated.
+End Refining_Separated
*)
(* end hide *)
include "ftc/Partitions.ma".
(* UNEXPORTED
-Section Separating__Separated.
+Section Separating__Separated
*)
-inline "cic:/CoRN/ftc/RefSeparated/a.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/a.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/b.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/b.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/Hab.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/I.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/I.con" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/F.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/F.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/contF.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/incF.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/incF.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/Hab'.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hab'.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/m.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/m.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/n.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/n.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/P.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/P.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/R.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/R.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/HP.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HP.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/HR.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/HR.var" "Separating__Separated__".
inline "cic:/CoRN/ftc/RefSeparated/RS_pos_n.con".
inline "cic:/CoRN/ftc/RefSeparated/RS_pos_m.con".
-inline "cic:/CoRN/ftc/RefSeparated/alpha.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/alpha.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/Halpha.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Halpha.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/e.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/e.con" "Separating__Separated__".
inline "cic:/CoRN/ftc/RefSeparated/RS_He.con".
-inline "cic:/CoRN/ftc/RefSeparated/contF'.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/contF'.con" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/d.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/d.con" "Separating__Separated__".
inline "cic:/CoRN/ftc/RefSeparated/RS_Hd.con".
inline "cic:/CoRN/ftc/RefSeparated/RS_Hd'.con".
-inline "cic:/CoRN/ftc/RefSeparated/csi.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/csi.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/Hcsi.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Hcsi.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/M.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/M.con" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/deltaP.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaP.con" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/deltaR.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/deltaR.con" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/delta.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/delta.con" "Separating__Separated__".
inline "cic:/CoRN/ftc/RefSeparated/RS_delta_deltaP.con".
inline "cic:/CoRN/ftc/RefSeparated/RS_delta_pos.con".
(* UNEXPORTED
-Section Defining_ai'.
+Section Defining_ai'
*)
-inline "cic:/CoRN/ftc/RefSeparated/i.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/i.var" "Separating__Separated__Defining_ai'__".
-inline "cic:/CoRN/ftc/RefSeparated/Hi.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi.var" "Separating__Separated__Defining_ai'__".
inline "cic:/CoRN/ftc/RefSeparated/separation_conseq.con".
-inline "cic:/CoRN/ftc/RefSeparated/pred1.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred1.con" "Separating__Separated__Defining_ai'__".
-inline "cic:/CoRN/ftc/RefSeparated/pred2.con".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/pred2.con" "Separating__Separated__Defining_ai'__".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_aux_lemma.con".
-inline "cic:/CoRN/ftc/RefSeparated/Hi0.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hi0.var" "Separating__Separated__Defining_ai'__".
-inline "cic:/CoRN/ftc/RefSeparated/Hin.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/Defining_ai'/Hin.var" "Separating__Separated__Defining_ai'__".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun_i.con".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_ap.con".
(* UNEXPORTED
-End Defining_ai'.
+End Defining_ai'
*)
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_fun.con".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_lemma.con".
-inline "cic:/CoRN/ftc/RefSeparated/g.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/g.var" "Separating__Separated__".
-inline "cic:/CoRN/ftc/RefSeparated/gP.var".
+inline "cic:/CoRN/ftc/RefSeparated/Separating__Separated/gP.var" "Separating__Separated__".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_points.con".
inline "cic:/CoRN/ftc/RefSeparated/sep__sep_Mesh.con".
(* UNEXPORTED
-End Separating__Separated.
+End Separating__Separated
*)
(* end hide *)
include "ftc/Partitions.ma".
(* UNEXPORTED
-Section Separating_Partition.
+Section Separating_Partition
*)
-inline "cic:/CoRN/ftc/RefSeparating/a.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/a.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/b.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/b.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/Hab.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/I.con".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/I.con" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/F.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/F.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/contF.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/contF.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/incF.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/incF.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/Hab'.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab'.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/n.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/n.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/P.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/P.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/alpha.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/alpha.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/Halpha.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Halpha.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/csi.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/csi.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/Hcsi.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hcsi.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/M.con".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/M.con" "Separating_Partition__".
inline "cic:/CoRN/ftc/RefSeparating/RS'_pos_n.con".
inline "cic:/CoRN/ftc/RefSeparating/SPap_n.con".
-inline "cic:/CoRN/ftc/RefSeparating/delta.con".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/delta.con" "Separating_Partition__".
inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_pos.con".
inline "cic:/CoRN/ftc/RefSeparating/RS'_delta_csi.con".
-inline "cic:/CoRN/ftc/RefSeparating/Hab''.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/Hab''.var" "Separating_Partition__".
inline "cic:/CoRN/ftc/RefSeparating/sep__part_lemma.con".
inline "cic:/CoRN/ftc/RefSeparating/sep__part_mon_Mesh.con".
-inline "cic:/CoRN/ftc/RefSeparating/g.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/g.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/gP.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP.var" "Separating_Partition__".
-inline "cic:/CoRN/ftc/RefSeparating/gP'.var".
+inline "cic:/CoRN/ftc/RefSeparating/Separating_Partition/gP'.var" "Separating_Partition__".
inline "cic:/CoRN/ftc/RefSeparating/sep__part_pts.con".
inline "cic:/CoRN/ftc/RefSeparating/sep__part_Sum.con".
(* UNEXPORTED
-End Separating_Partition.
+End Separating_Partition
*)
(* end hide *)
include "ftc/MoreFunctions.ma".
(* UNEXPORTED
-Section Rolle.
+Section Rolle
*)
(*#* *Rolle's Theorem
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/a.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/a.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/b.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hab'.var" "Rolle__".
-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".
+inline "cic:/CoRN/ftc/Rolle/Rolle/F.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/F'.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/derF.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/derF.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Ha.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Ha.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/Hb.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Hb.var" "Rolle__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/Fab.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/Fab.var" "Rolle__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/Rolle/e.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/e.var" "Rolle__".
-inline "cic:/CoRN/ftc/Rolle/He.var".
+inline "cic:/CoRN/ftc/Rolle/Rolle/He.var" "Rolle__".
-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__".
(* NOTATION
Notation cp := (compact_part a b Hab' d Hd).
*)
-inline "cic:/CoRN/ftc/Rolle/Rolle_lemma4.con".
+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".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/a.var" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/b.var" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/Hab'.var" "Law_of_the_Mean__".
(* 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".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F.var" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/F'.var" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/HF.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HF.var" "Law_of_the_Mean__".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/HA.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HA.var" "Law_of_the_Mean__".
-inline "cic:/CoRN/ftc/Rolle/HB.var".
+inline "cic:/CoRN/ftc/Rolle/Law_of_the_Mean/HB.var" "Law_of_the_Mean__".
(* 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".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/a.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Rolle/b.var".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/b.var" "Corollaries__".
-inline "cic:/CoRN/ftc/Rolle/Hab'.var".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/Hab'.var" "Corollaries__".
(* 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".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/F.var" "Corollaries__".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/HF.var".
+inline "cic:/CoRN/ftc/Rolle/Corollaries/HF.var" "Corollaries__".
(* 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".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/I.var" "Generalizations__".
-inline "cic:/CoRN/ftc/Rolle/pI.var".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/pI.var" "Generalizations__".
-inline "cic:/CoRN/ftc/Rolle/F.var".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/F.var" "Generalizations__".
-inline "cic:/CoRN/ftc/Rolle/F'.var".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/F'.var" "Generalizations__".
(* begin show *)
-inline "cic:/CoRN/ftc/Rolle/derF.var".
+inline "cic:/CoRN/ftc/Rolle/Generalizations/derF.var" "Generalizations__".
(* 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
*)
include "ftc/CalculusTheorems.ma".
(* UNEXPORTED
-Section IVT'.
+Section IVT'
*)
(*#* ** Strong IVT for partial functions
The same notations and conventions apply as before.
*)
-inline "cic:/CoRN/ftc/StrongIVT/a.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/a.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/b.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/b.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/Hab'.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hab'.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/Hab.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hab.var" "IVT'__".
(* begin hide *)
-inline "cic:/CoRN/ftc/StrongIVT/I.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/I.con" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/I'.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/I'.con" "IVT'__".
(* end hide *)
-inline "cic:/CoRN/ftc/StrongIVT/F.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/F.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/contF.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/contF.var" "IVT'__".
(* begin hide *)
-inline "cic:/CoRN/ftc/StrongIVT/incF.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/incF.con" "IVT'__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/StrongIVT/incrF.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/incrF.var" "IVT'__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/StrongIVT/Ha.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Ha.con" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/Hb.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hb.con" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/HFab'.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/HFab'.con" "IVT'__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/StrongIVT/z.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/z.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/Haz.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Haz.var" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/Hzb.var".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/Hzb.var" "IVT'__".
(* end show *)
inline "cic:/CoRN/ftc/StrongIVT/b'_seq_Cauchy.con".
-inline "cic:/CoRN/ftc/StrongIVT/xa.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/xa.con" "IVT'__".
-inline "cic:/CoRN/ftc/StrongIVT/xb.con".
+inline "cic:/CoRN/ftc/StrongIVT/IVT'/xb.con" "IVT'__".
inline "cic:/CoRN/ftc/StrongIVT/a'_seq_b'_seq_lim.con".
inline "cic:/CoRN/ftc/StrongIVT/IVT'_I.con".
(* UNEXPORTED
-End IVT'.
+End IVT'
*)
(*#* **Other formulations
*)
(* UNEXPORTED
-Section More_Taylor_Defs.
+Section More_Taylor_Defs
*)
(*#* **General case
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Taylor/I.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/I.var" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/pI.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/pI.var" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/F.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/F.var" "More_Taylor_Defs__".
(* begin show *)
-inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/deriv_Sn.con" "More_Taylor_Defs__".
(* end show *)
-inline "cic:/CoRN/ftc/Taylor/a.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/a.var" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/b.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/b.var" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/Ha.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Ha.var" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/Hb.var".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/Hb.var" "More_Taylor_Defs__".
(* begin show *)
-inline "cic:/CoRN/ftc/Taylor/fi.con".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/fi.con" "More_Taylor_Defs__".
-inline "cic:/CoRN/ftc/Taylor/funct_i.con".
+inline "cic:/CoRN/ftc/Taylor/More_Taylor_Defs/funct_i.con" "More_Taylor_Defs__".
(* end show *)
inline "cic:/CoRN/ftc/Taylor/Taylor'.con".
(* UNEXPORTED
-End More_Taylor_Defs.
+End More_Taylor_Defs
*)
(* UNEXPORTED
-Section Taylor_Theorem.
+Section Taylor_Theorem
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/Taylor/I.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/I.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/pI.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/pI.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/F.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/n.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/n.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/f.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/f.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/goodF.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/goodF'.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/goodF'.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/derF.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/F'.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/F'.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/derF'.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/derF'.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/a.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/a.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/b.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/b.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/Ha.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Ha.var" "Taylor_Theorem__".
-inline "cic:/CoRN/ftc/Taylor/Hb.var".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/Hb.var" "Taylor_Theorem__".
(* begin show *)
-inline "cic:/CoRN/ftc/Taylor/funct_i.con".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/funct_i.con" "Taylor_Theorem__".
inline "cic:/CoRN/ftc/Taylor/Taylor_Seq.con".
-inline "cic:/CoRN/ftc/Taylor/deriv_Sn.con".
+inline "cic:/CoRN/ftc/Taylor/Taylor_Theorem/deriv_Sn.con" "Taylor_Theorem__".
(* end show *)
inline "cic:/CoRN/ftc/Taylor/Taylor.con".
(* UNEXPORTED
-End Taylor_Theorem.
+End Taylor_Theorem
*)
*)
(* UNEXPORTED
-Section Taylor_Defs.
+Section Taylor_Defs
*)
(*#* *Taylor's Theorem
[[Min(a,b),Max(a,b)]].
*)
-inline "cic:/CoRN/ftc/TaylorLemma/a.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/a.var" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/b.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/b.var" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/Hap.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hap.var" "Taylor_Defs__".
(* 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".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/F.var" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/Ha.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Ha.var" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/Hb.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/Hb.var" "Taylor_Defs__".
(* 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/TL_compact_a.con".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_a.con" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/TL_compact_b.con".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/TL_compact_b.con" "Taylor_Defs__".
(* NOTATION
Notation A := (Build_subcsetoid_crr IR _ _ TL_compact_a).
(* 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".
(* 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".
(* 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.
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_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.
%\end{convention}%
*)
-inline "cic:/CoRN/ftc/TaylorLemma/e.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/e.var" "Taylor_Defs__".
-inline "cic:/CoRN/ftc/TaylorLemma/He.var".
+inline "cic:/CoRN/ftc/TaylorLemma/Taylor_Defs/He.var" "Taylor_Defs__".
(* begin 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 *)
inline "cic:/CoRN/ftc/TaylorLemma/Taylor_lemma.con".
(* UNEXPORTED
-End Taylor_Defs.
+End Taylor_Defs
*)
*)
(* UNEXPORTED
-Section Lemma1.
+Section Lemma1
*)
-inline "cic:/CoRN/ftc/WeakIVT/a.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/a.var" "Lemma1__".
-inline "cic:/CoRN/ftc/WeakIVT/b.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/b.var" "Lemma1__".
-inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/Hab.var" "Lemma1__".
(* begin hide *)
-inline "cic:/CoRN/ftc/WeakIVT/I.con".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/I.con" "Lemma1__".
(* end hide *)
-inline "cic:/CoRN/ftc/WeakIVT/F.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/F.var" "Lemma1__".
-inline "cic:/CoRN/ftc/WeakIVT/contF.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma1/contF.var" "Lemma1__".
(*#* **First Lemmas
inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_lft.con".
(* UNEXPORTED
-End Lemma1.
+End Lemma1
*)
(* UNEXPORTED
-Section Lemma2.
+Section Lemma2
*)
-inline "cic:/CoRN/ftc/WeakIVT/a.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/a.var" "Lemma2__".
-inline "cic:/CoRN/ftc/WeakIVT/b.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/b.var" "Lemma2__".
-inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/Hab.var" "Lemma2__".
(* begin hide *)
-inline "cic:/CoRN/ftc/WeakIVT/I.con".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/I.con" "Lemma2__".
(* end hide *)
-inline "cic:/CoRN/ftc/WeakIVT/F.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/F.var" "Lemma2__".
-inline "cic:/CoRN/ftc/WeakIVT/contF.var".
+inline "cic:/CoRN/ftc/WeakIVT/Lemma2/contF.var" "Lemma2__".
(*#*
If [f(b) [<] f(a)], a similar result holds:
inline "cic:/CoRN/ftc/WeakIVT/Weak_IVT_ap_rht.con".
(* UNEXPORTED
-End Lemma2.
+End Lemma2
*)
(* UNEXPORTED
-Section IVT.
+Section IVT
*)
(*#* **The IVT
converge to [x0] such that [f(x0) [=] z].
*)
-inline "cic:/CoRN/ftc/WeakIVT/a.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/a.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/b.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/b.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/Hab'.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Hab'.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/Hab.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Hab.var" "IVT__".
(* begin hide *)
-inline "cic:/CoRN/ftc/WeakIVT/I.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/I.con" "IVT__".
(* end hide *)
-inline "cic:/CoRN/ftc/WeakIVT/F.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/F.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/contF.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/contF.var" "IVT__".
(* begin hide *)
-inline "cic:/CoRN/ftc/WeakIVT/incF.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/incF.con" "IVT__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/WeakIVT/incrF.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/incrF.var" "IVT__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/ftc/WeakIVT/Ha.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Ha.con" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/Hb.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Hb.con" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/HFab'.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/HFab'.con" "IVT__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/ftc/WeakIVT/z.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/z.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/Haz.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Haz.var" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/Hzb.var".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/Hzb.var" "IVT__".
(* end show *)
inline "cic:/CoRN/ftc/WeakIVT/b_seq_Cauchy.con".
-inline "cic:/CoRN/ftc/WeakIVT/xa.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/xa.con" "IVT__".
-inline "cic:/CoRN/ftc/WeakIVT/xb.con".
+inline "cic:/CoRN/ftc/WeakIVT/IVT/xb.con" "IVT__".
inline "cic:/CoRN/ftc/WeakIVT/a_seq_b_seq_lim.con".
inline "cic:/CoRN/ftc/WeakIVT/IVT_I.con".
(* UNEXPORTED
-End IVT.
+End IVT
*)
include "metrics/Equiv.ma".
(* UNEXPORTED
-Section Definition_MS.
+Section Definition_MS
*)
(*#* **Definition of Metric Space
coercion cic:/matita/CoRN-Decl/metrics/CMetricSpaces/scms_crr.con 0 (* compounds *).
(* UNEXPORTED
-End Definition_MS.
+End Definition_MS
*)
(* UNEXPORTED
-Section MS_basics.
+Section MS_basics
*)
(*#* **Metric Space basics
inline "cic:/CoRN/metrics/CMetricSpaces/is_CMetricSpace_diag_zero.con".
(* UNEXPORTED
-End MS_basics.
+End MS_basics
*)
(* UNEXPORTED
-Section prodandsub.
+Section prodandsub
*)
(*#* **Product-Metric-Spaces and Sub-Metric-Spaces
*)
(* UNEXPORTED
-End prodandsub.
+End prodandsub
*)
(* UNEXPORTED
-Section Zeroff.
+Section Zeroff
*)
(*#* **Pseudo Metric Spaces vs Metric Spaces
inline "cic:/CoRN/metrics/CMetricSpaces/Quotient_pres_CMetricSpace.con".
(* UNEXPORTED
-End Zeroff.
+End Zeroff
*)
(* UNEXPORTED
-Section Limitt.
+Section Limitt
*)
(*#* **Limit
inline "cic:/CoRN/metrics/CMetricSpaces/unique_MSseqLim.con".
(* UNEXPORTED
-End Limitt.
+End Limitt
*)
include "metrics/Prod_Sub.ma".
(* UNEXPORTED
-Section lists.
+Section lists
*)
(*#* **Lists
inline "cic:/CoRN/metrics/CPMSTheory/map_member.con".
(* UNEXPORTED
-End lists.
+End lists
*)
(* UNEXPORTED
-Section loc_and_bound.
+Section loc_and_bound
*)
(*#* **Pseudo Metric Space theory
inline "cic:/CoRN/metrics/CPMSTheory/well_contained.con".
(* UNEXPORTED
-End loc_and_bound.
+End loc_and_bound
*)
*)
(* UNEXPORTED
-Section Relations.
+Section Relations
*)
(*#* **Relations necessary for Pseudo Metric Spaces and Metric Spaces
%\end{convention}%
*)
-inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var".
+inline "cic:/CoRN/metrics/CPseudoMSpaces/Relations/A.var" "Relations__".
-inline "cic:/CoRN/metrics/CPseudoMSpaces/d.var".
+inline "cic:/CoRN/metrics/CPseudoMSpaces/Relations/d.var" "Relations__".
(* UNEXPORTED
Set Implicit Arguments.
inline "cic:/CoRN/metrics/CPseudoMSpaces/apdiag_imp_grzero.con".
(* UNEXPORTED
-End Relations.
+End Relations
*)
(* UNEXPORTED
-Section Definition_PsMS0.
+Section Definition_PsMS0
*)
(*#* **Definition of Pseudo Metric Space
coercion cic:/matita/CoRN-Decl/metrics/CPseudoMSpaces/cms_crr.con 0 (* compounds *).
(* UNEXPORTED
-End Definition_PsMS0.
+End Definition_PsMS0
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section PsMS_axioms.
+Section PsMS_axioms
*)
(*#* **Pseudo Metric Space axioms
%\end{convention}%
*)
-inline "cic:/CoRN/metrics/CPseudoMSpaces/A.var".
+inline "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_axioms/A.var" "PsMS_axioms__".
inline "cic:/CoRN/metrics/CPseudoMSpaces/CPsMetricSpace_is_CPsMetricSpace.con".
inline "cic:/CoRN/metrics/CPseudoMSpaces/d_tri_ineq.con".
(* UNEXPORTED
-End PsMS_axioms.
+End PsMS_axioms
*)
(* UNEXPORTED
-Section PsMS_basics.
+Section PsMS_basics
*)
(*#* **Pseudo Metric Space basics
%\end{convention}%
*)
-inline "cic:/CoRN/metrics/CPseudoMSpaces/Y.var".
+inline "cic:/CoRN/metrics/CPseudoMSpaces/PsMS_basics/Y.var" "PsMS_basics__".
inline "cic:/CoRN/metrics/CPseudoMSpaces/rev_tri_ineq.con".
inline "cic:/CoRN/metrics/CPseudoMSpaces/is_CPsMetricSpace_diag_zero.con".
(* UNEXPORTED
-End PsMS_basics.
+End PsMS_basics
*)
(* UNEXPORTED
-Section Zerof.
+Section Zerof
*)
(*#* **Zero function
inline "cic:/CoRN/metrics/CPseudoMSpaces/zf_as_CPsMetricSpace.con".
(* UNEXPORTED
-End Zerof.
+End Zerof
*)
include "metrics/CPseudoMSpaces.ma".
(* UNEXPORTED
-Section Continuous_functions.
+Section Continuous_functions
*)
(*#* **Continuous functions, uniformly continuous functions and Lipschitz functions
%\end{convention}%
*)
-inline "cic:/CoRN/metrics/ContFunctions/A.var".
+inline "cic:/CoRN/metrics/ContFunctions/Continuous_functions/A.var" "Continuous_functions__".
-inline "cic:/CoRN/metrics/ContFunctions/B.var".
+inline "cic:/CoRN/metrics/ContFunctions/Continuous_functions/B.var" "Continuous_functions__".
(*#*
We will look at some notions of continuous functions.
inline "cic:/CoRN/metrics/ContFunctions/lipschitz'.con".
(* UNEXPORTED
-End Continuous_functions.
+End Continuous_functions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(* begin hide *)
inline "cic:/CoRN/metrics/ContFunctions/lipschitz_imp_uni_continuous.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section Identity.
+Section Identity
*)
(*#* **Identity
inline "cic:/CoRN/metrics/ContFunctions/id_is_continuous.con".
(* UNEXPORTED
-End Identity.
+End Identity
*)
(* UNEXPORTED
-Section Constant.
+Section Constant
*)
(*#* **Constant functions
Hence it is uniformly continuous and continuous.
*)
-inline "cic:/CoRN/metrics/ContFunctions/B.var".
+inline "cic:/CoRN/metrics/ContFunctions/Constant/B.var" "Constant__".
-inline "cic:/CoRN/metrics/ContFunctions/X.var".
+inline "cic:/CoRN/metrics/ContFunctions/Constant/X.var" "Constant__".
inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_lipschitz.con".
inline "cic:/CoRN/metrics/ContFunctions/const_fun_is_continuous.con".
(* UNEXPORTED
-End Constant.
+End Constant
*)
(* UNEXPORTED
-Section Composition.
+Section Composition
*)
(*#* **Composition
again Lipschitz/uniformly continuous/continuous.
*)
-inline "cic:/CoRN/metrics/ContFunctions/X.var".
+inline "cic:/CoRN/metrics/ContFunctions/Composition/X.var" "Composition__".
-inline "cic:/CoRN/metrics/ContFunctions/B.var".
+inline "cic:/CoRN/metrics/ContFunctions/Composition/B.var" "Composition__".
-inline "cic:/CoRN/metrics/ContFunctions/f.var".
+inline "cic:/CoRN/metrics/ContFunctions/Composition/f.var" "Composition__".
-inline "cic:/CoRN/metrics/ContFunctions/C.var".
+inline "cic:/CoRN/metrics/ContFunctions/Composition/C.var" "Composition__".
-inline "cic:/CoRN/metrics/ContFunctions/g.var".
+inline "cic:/CoRN/metrics/ContFunctions/Composition/g.var" "Composition__".
inline "cic:/CoRN/metrics/ContFunctions/comp_resp_lipschitz.con".
inline "cic:/CoRN/metrics/ContFunctions/comp_resp_continuous.con".
(* UNEXPORTED
-End Composition.
+End Composition
*)
(* UNEXPORTED
-Section Limit.
+Section Limit
*)
(*#* **Limit
inline "cic:/CoRN/metrics/ContFunctions/continuous'_imp_seqcontinuous'.con".
(* UNEXPORTED
-End Limit.
+End Limit
*)
include "metrics/IR_CPMSpace.ma".
(* UNEXPORTED
-Section equivalent.
+Section equivalent
*)
(*#* **Equivalent Pseudo Metric Spaces
inline "cic:/CoRN/metrics/Equiv/MSequivalent_discr.con".
(* UNEXPORTED
-End equivalent.
+End equivalent
*)
include "metrics/ContFunctions.ma".
(* UNEXPORTED
-Section Reals.
+Section Reals
*)
(*#* **Real numbers
inline "cic:/CoRN/metrics/IR_CPMSpace/IR_as_CPsMetricSpace.con".
-inline "cic:/CoRN/metrics/IR_CPMSpace/X.var".
+inline "cic:/CoRN/metrics/IR_CPMSpace/Reals/X.var" "Reals__".
inline "cic:/CoRN/metrics/IR_CPMSpace/rev_tri_ineq'.con".
inline "cic:/CoRN/metrics/IR_CPMSpace/d_is_continuous.con".
(* UNEXPORTED
-End Reals.
+End Reals
*)
(* UNEXPORTED
-Section Addition.
+Section Addition
*)
(*#* **Addition of continuous functions
inline "cic:/CoRN/metrics/IR_CPMSpace/plus_resp_continuous.con".
(* UNEXPORTED
-End Addition.
+End Addition
*)
include "metrics/IR_CPMSpace.ma".
(* UNEXPORTED
-Section prodpsmetrics.
+Section prodpsmetrics
*)
(*#* **Product-Pseudo-Metric-Spaces
inline "cic:/CoRN/metrics/Prod_Sub/Prod0CPsMetricSpace.con".
(* UNEXPORTED
-End prodpsmetrics.
+End prodpsmetrics
*)
(* UNEXPORTED
-Section subpsmetrics.
+Section subpsmetrics
*)
(*#* **Sub-Pseudo-Metric-Spaces
inline "cic:/CoRN/metrics/Prod_Sub/dsub'_uni_continuous''.con".
(* UNEXPORTED
-End subpsmetrics.
+End subpsmetrics
*)
inverse an de constants 0 and 1. *)
(* UNEXPORTED
-Section Q.
+Section Q
*)
inline "cic:/CoRN/model/structures/Qsec/Q.ind".
inline "cic:/CoRN/model/structures/Qsec/Qinv.con".
(* UNEXPORTED
-End Q.
+End Q
*)
(* NOTATION
include "algebra/Expon.ma".
(* UNEXPORTED
-Section LUBP.
+Section LUBP
*)
-inline "cic:/CoRN/reals/Bridges_LUB/R1.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/R1.var" "LUBP__".
(* SUBSECTION ON GENRAL DEFINITIONS *)
(* UNEXPORTED
-Section lub_definitions.
+Section lub_definitions
*)
-inline "cic:/CoRN/reals/Bridges_LUB/OF.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/OF.var" "LUBP__lub_definitions__".
-inline "cic:/CoRN/reals/Bridges_LUB/SS.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/lub_definitions/SS.var" "LUBP__lub_definitions__".
inline "cic:/CoRN/reals/Bridges_LUB/member.con".
inline "cic:/CoRN/reals/Bridges_LUB/Pinfimum.con".
(* UNEXPORTED
-End lub_definitions.
+End lub_definitions
*)
(* MAIN SECTION *)
(* UNEXPORTED
-Section upper_bound_sequence.
+Section upper_bound_sequence
*)
-inline "cic:/CoRN/reals/Bridges_LUB/A.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/A.var" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/is_inhabitted.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/is_inhabitted.var" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/bounded_above.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/bounded_above.var" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/located.var".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/located.var" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/s.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/s.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/Ps.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Ps.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/b0.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/b0.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/Pb0.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/Pb0.con" "LUBP__upper_bound_sequence__".
inline "cic:/CoRN/reals/Bridges_LUB/b0_is_upper_bound.con".
inline "cic:/CoRN/reals/Bridges_LUB/s_inhabits_A.con".
-inline "cic:/CoRN/reals/Bridges_LUB/dstart_l.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_l.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/dstart_r.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/dstart_r.con" "LUBP__upper_bound_sequence__".
inline "cic:/CoRN/reals/Bridges_LUB/dl_less_dr.con".
inline "cic:/CoRN/reals/Bridges_LUB/dIntrvl.con".
-inline "cic:/CoRN/reals/Bridges_LUB/U.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/U.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/V.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/V.con" "LUBP__upper_bound_sequence__".
-inline "cic:/CoRN/reals/Bridges_LUB/W.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/W.con" "LUBP__upper_bound_sequence__".
inline "cic:/CoRN/reals/Bridges_LUB/delta_dIntrvl.con".
inline "cic:/CoRN/reals/Bridges_LUB/U_as_CauchySeq.con".
-inline "cic:/CoRN/reals/Bridges_LUB/B.con".
+inline "cic:/CoRN/reals/Bridges_LUB/LUBP/upper_bound_sequence/B.con" "LUBP__upper_bound_sequence__".
inline "cic:/CoRN/reals/Bridges_LUB/U_minus_V.con".
inline "cic:/CoRN/reals/Bridges_LUB/cauchy_gives_lub.con".
(* UNEXPORTED
-End upper_bound_sequence.
+End upper_bound_sequence
*)
(* UNEXPORTED
-End LUBP.
+End LUBP
*)
(* end hide *)
inline "cic:/CoRN/reals/Bridges_iso/le_witness_informative.con".
(* UNEXPORTED
-Section bridges_axioms_imply_ours.
+Section bridges_axioms_imply_ours
*)
-inline "cic:/CoRN/reals/Bridges_iso/OF.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/OF.var" "bridges_axioms_imply_ours__".
-inline "cic:/CoRN/reals/Bridges_iso/lubp.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/lubp.var" "bridges_axioms_imply_ours__".
-inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/is_Archimedes.var" "bridges_axioms_imply_ours__".
inline "cic:/CoRN/reals/Bridges_iso/is_Archimedes'.con".
(* UNEXPORTED
-Section proofs_in_TCS.
+Section proofs_in_TCS
*)
inline "cic:/CoRN/reals/Bridges_iso/leEq_geEq.con".
inline "cic:/CoRN/reals/Bridges_iso/glbp.con".
(* UNEXPORTED
-Section supremum.
+Section supremum
*)
-inline "cic:/CoRN/reals/Bridges_iso/P.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__".
inline "cic:/CoRN/reals/Bridges_iso/inequality1.con".
inline "cic:/CoRN/reals/Bridges_iso/Pkaf.con".
-inline "cic:/CoRN/reals/Bridges_iso/is_finite_P.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_finite_P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__".
inline "cic:/CoRN/reals/Bridges_iso/card.con".
inline "cic:/CoRN/reals/Bridges_iso/Pindeks.con".
-inline "cic:/CoRN/reals/Bridges_iso/is_onto_seq_P.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/is_onto_seq_P.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__".
inline "cic:/CoRN/reals/Bridges_iso/P_is_inhabited.con".
inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1a.con".
-inline "cic:/CoRN/reals/Bridges_iso/P_is_strongly_extensional.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/supremum/P_is_strongly_extensional.var" "bridges_axioms_imply_ours__proofs_in_TCS__supremum__".
inline "cic:/CoRN/reals/Bridges_iso/bridges_lemma1b.con".
(* UNEXPORTED
-End supremum.
+End supremum
*)
(*#**********************************)
(*#**********************************)
(* UNEXPORTED
-Section Every_Cauchy_Sequence_is_bounded.
+Section Every_Cauchy_Sequence_is_bounded
*)
inline "cic:/CoRN/reals/Bridges_iso/seq2set.con".
-inline "cic:/CoRN/reals/Bridges_iso/g.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g.var" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
-inline "cic:/CoRN/reals/Bridges_iso/g_.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
-inline "cic:/CoRN/reals/Bridges_iso/pg.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
-inline "cic:/CoRN/reals/Bridges_iso/P.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/Every_Cauchy_Sequence_is_bounded/P.con" "bridges_axioms_imply_ours__proofs_in_TCS__Every_Cauchy_Sequence_is_bounded__".
inline "cic:/CoRN/reals/Bridges_iso/fin_is_fin.con".
inline "cic:/CoRN/reals/Bridges_iso/tail_seq.con".
(* UNEXPORTED
-End Every_Cauchy_Sequence_is_bounded.
+End Every_Cauchy_Sequence_is_bounded
*)
-inline "cic:/CoRN/reals/Bridges_iso/g.var".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g.var" "bridges_axioms_imply_ours__proofs_in_TCS__".
-inline "cic:/CoRN/reals/Bridges_iso/g_.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/g_.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
-inline "cic:/CoRN/reals/Bridges_iso/pg.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/pg.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
-inline "cic:/CoRN/reals/Bridges_iso/sup_tail.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/sup_tail.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
inline "cic:/CoRN/reals/Bridges_iso/sup_tail_leEq.con".
inline "cic:/CoRN/reals/Bridges_iso/sup_tail_as_Cauchy.con".
-inline "cic:/CoRN/reals/Bridges_iso/L.con".
+inline "cic:/CoRN/reals/Bridges_iso/bridges_axioms_imply_ours/proofs_in_TCS/L.con" "bridges_axioms_imply_ours__proofs_in_TCS__".
inline "cic:/CoRN/reals/Bridges_iso/sup_tail_decrease.con".
inline "cic:/CoRN/reals/Bridges_iso/lubp_gives_Cauchy.con".
(* UNEXPORTED
-End proofs_in_TCS.
+End proofs_in_TCS
*)
inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_is_CReals.con".
inline "cic:/CoRN/reals/Bridges_iso/Bridges_R_as_CReals.con".
(* UNEXPORTED
-End bridges_axioms_imply_ours.
+End bridges_axioms_imply_ours
*)
(* end hide *)
include "reals/CReals1.ma".
(* UNEXPORTED
-Section CMetric_Fields.
+Section CMetric_Fields
*)
(*#* *Metric Fields *)
coercion cic:/matita/CoRN-Decl/reals/CMetricFields/cmf_crr.con 0 (* compounds *).
(* UNEXPORTED
-End CMetric_Fields.
+End CMetric_Fields
*)
(* NOTATION
*)
(* UNEXPORTED
-Section basics.
+Section basics
*)
inline "cic:/CoRN/reals/CMetricFields/MAbs_one.con".
(* end hide *)
(* UNEXPORTED
-End basics.
+End basics
*)
(* UNEXPORTED
-Section CMetric_Field_Cauchy.
+Section CMetric_Field_Cauchy
*)
-inline "cic:/CoRN/reals/CMetricFields/F.var".
+inline "cic:/CoRN/reals/CMetricFields/CMetric_Field_Cauchy/F.var" "CMetric_Field_Cauchy__".
(*#*
%\begin{convention}% Let [F:CMetricField].
inline "cic:/CoRN/reals/CMetricFields/is_MCauchyCompl.con".
(* UNEXPORTED
-End CMetric_Field_Cauchy.
+End CMetric_Field_Cauchy
*)
(* UNEXPORTED
include "algebra/CPoly_ApZero.ma".
(* UNEXPORTED
-Section More_Cauchy_Props.
+Section More_Cauchy_Props
*)
(*#* **Miscellaneous
inline "cic:/CoRN/reals/CReals1/Lim_abs.con".
(* UNEXPORTED
-End More_Cauchy_Props.
+End More_Cauchy_Props
*)
(* UNEXPORTED
-Section Subsequences.
+Section Subsequences
*)
(*#* *** Subsequences
[seq2] is monotonous.
*)
-inline "cic:/CoRN/reals/CReals1/seq1.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/seq1.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/seq2.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/seq2.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/f.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/f.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/monF.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/monF.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/crescF.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/crescF.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/subseq.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/subseq.var" "Subsequences__".
-inline "cic:/CoRN/reals/CReals1/mon_seq2.var".
+inline "cic:/CoRN/reals/CReals1/Subsequences/mon_seq2.var" "Subsequences__".
inline "cic:/CoRN/reals/CReals1/unbnd_f.con".
(* begin hide *)
-inline "cic:/CoRN/reals/CReals1/mon_F'.con".
+inline "cic:/CoRN/reals/CReals1/Subsequences/mon_F'.con" "Subsequences__".
(* end hide *)
inline "cic:/CoRN/reals/CReals1/Cprop2_subseq_imp_Cprop2_seq.con".
(* UNEXPORTED
-End Subsequences.
+End Subsequences
*)
(* UNEXPORTED
-Section Cauchy_Subsequences.
+Section Cauchy_Subsequences
*)
-inline "cic:/CoRN/reals/CReals1/seq1.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq1.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/seq2.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/seq2.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/f.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/f.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/monF.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/monF.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/crescF.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/crescF.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/subseq.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/subseq.var" "Cauchy_Subsequences__".
-inline "cic:/CoRN/reals/CReals1/mon_seq2.var".
+inline "cic:/CoRN/reals/CReals1/Cauchy_Subsequences/mon_seq2.var" "Cauchy_Subsequences__".
inline "cic:/CoRN/reals/CReals1/Lim_seq_eq_Lim_subseq.con".
inline "cic:/CoRN/reals/CReals1/Lim_subseq_eq_Lim_seq.con".
(* UNEXPORTED
-End Cauchy_Subsequences.
+End Cauchy_Subsequences
*)
(* UNEXPORTED
-Section Properties_of_Exponentiation.
+Section Properties_of_Exponentiation
*)
(*#* *** More properties of Exponentiation
inline "cic:/CoRN/reals/CReals1/qi_lim_zero.con".
(* UNEXPORTED
-End Properties_of_Exponentiation.
+End Properties_of_Exponentiation
*)
(*#* *** [IR] has characteristic zero *)
*)
(* UNEXPORTED
-Section Sums_over_Reals.
+Section Sums_over_Reals
*)
-inline "cic:/CoRN/reals/CSumsReals/c.var".
+inline "cic:/CoRN/reals/CSumsReals/Sums_over_Reals/c.var" "Sums_over_Reals__".
inline "cic:/CoRN/reals/CSumsReals/Sum0_c_exp.con".
*)
(* UNEXPORTED
-End Sums_over_Reals.
+End Sums_over_Reals
*)
(* UNEXPORTED
(* end hide *)
(* UNEXPORTED
-Section CReals_axioms.
+Section CReals_axioms
*)
(*#* ** [CReals] axioms *)
inline "cic:/CoRN/reals/CauchySeq/CauchySeqR.con".
(* UNEXPORTED
-End CReals_axioms.
+End CReals_axioms
*)
(* UNEXPORTED
-Section Cauchy_Defs.
+Section Cauchy_Defs
*)
(*#* ** Cauchy sequences
inline "cic:/CoRN/reals/CauchySeq/Cauchy_prop4.con".
(* UNEXPORTED
-End Cauchy_Defs.
+End Cauchy_Defs
*)
(* UNEXPORTED
-Section Inequalities.
+Section Inequalities
*)
(*#* *** Inequalities of Limits
inline "cic:/CoRN/reals/CauchySeq/Lim_ap_imp_seq_ap'.con".
(* UNEXPORTED
-End Inequalities.
+End Inequalities
*)
(* UNEXPORTED
-Section Equiv_Cauchy.
+Section Equiv_Cauchy
*)
(*#* *** Equivalence of formulations of Cauchy *)
inline "cic:/CoRN/reals/CauchySeq/Lim_unique.con".
(* UNEXPORTED
-End Equiv_Cauchy.
+End Equiv_Cauchy
*)
(* UNEXPORTED
-Section Cauchy_props.
+Section Cauchy_props
*)
(*#* *** Properties of Cauchy sequences
inline "cic:/CoRN/reals/CauchySeq/Lim_mult.con".
(* UNEXPORTED
-End Cauchy_props.
+End Cauchy_props
*)
include "reals/CReals.ma".
(* UNEXPORTED
-Section R_CReals.
+Section R_CReals
*)
(*#* * The Real Number Structure
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Cauchy_CReals/F.var".
+inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F.var" "R_CReals__".
(* NOTATION
Notation "'R_COrdField''" := (R_COrdField F).
inline "cic:/CoRN/reals/Cauchy_CReals/conv_modulus.con".
-inline "cic:/CoRN/reals/Cauchy_CReals/T.con".
+inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/T.con" "R_CReals__".
(*#* We now assume our original field is archimedean and prove that the
resulting one is, too.
*)
-inline "cic:/CoRN/reals/Cauchy_CReals/F_is_archemaedian.var".
+inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/F_is_archemaedian.var" "R_CReals__".
inline "cic:/CoRN/reals/Cauchy_CReals/R_is_archemaedian.con".
(* begin hide *)
-inline "cic:/CoRN/reals/Cauchy_CReals/PT.con".
+inline "cic:/CoRN/reals/Cauchy_CReals/R_CReals/PT.con" "R_CReals__".
(* end hide *)
inline "cic:/CoRN/reals/Cauchy_CReals/R_as_CReals.con".
(* UNEXPORTED
-End R_CReals.
+End R_CReals
*)
include "reals/CPoly_Contin.ma".
(* UNEXPORTED
-Section Nested_Intervals.
+Section Nested_Intervals
*)
(*#* * Intermediate Value Theorem
%\end{convention}%
*)
-inline "cic:/CoRN/reals/IVT/a.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/a.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/b.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/b.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/a_mon.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/a_mon.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/b_mon.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/b_mon.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/a_b.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/a_b.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/b_a.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/b_a.var" "Nested_Intervals__".
inline "cic:/CoRN/reals/IVT/a_mon'.con".
(* begin hide *)
-inline "cic:/CoRN/reals/IVT/a'.con".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/a'.con" "Nested_Intervals__".
(* end hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/reals/IVT/f.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/f.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/f_contin.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_contin.var" "Nested_Intervals__".
inline "cic:/CoRN/reals/IVT/f_contin_pos.con".
(*#* Assume also that [forall i, f (a i) [<=] Zero [<=] f (b i)]. *)
-inline "cic:/CoRN/reals/IVT/f_a.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_a.var" "Nested_Intervals__".
-inline "cic:/CoRN/reals/IVT/f_b.var".
+inline "cic:/CoRN/reals/IVT/Nested_Intervals/f_b.var" "Nested_Intervals__".
inline "cic:/CoRN/reals/IVT/Cnested_intervals_zero.con".
(* UNEXPORTED
-End Nested_Intervals.
+End Nested_Intervals
*)
(* UNEXPORTED
-Section Bisection.
+Section Bisection
*)
(*#* ** Bissections *)
-inline "cic:/CoRN/reals/IVT/f.var".
+inline "cic:/CoRN/reals/IVT/Bisection/f.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/f_apzero_interval.var".
+inline "cic:/CoRN/reals/IVT/Bisection/f_apzero_interval.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/a.var".
+inline "cic:/CoRN/reals/IVT/Bisection/a.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/b.var".
+inline "cic:/CoRN/reals/IVT/Bisection/b.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/a_b.var".
+inline "cic:/CoRN/reals/IVT/Bisection/a_b.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/f_a.var".
+inline "cic:/CoRN/reals/IVT/Bisection/f_a.var" "Bisection__".
-inline "cic:/CoRN/reals/IVT/f_b.var".
+inline "cic:/CoRN/reals/IVT/Bisection/f_b.var" "Bisection__".
(*#*
%\begin{convention}% Let [Small] denote [Two[/]ThreeNZ], [lft] be [(Two[*]a[+]b) [/]ThreeNZ] and [rht] be [(a[+]Two[*]b) [/]ThreeNZ].
(* begin hide *)
-inline "cic:/CoRN/reals/IVT/Small.con".
+inline "cic:/CoRN/reals/IVT/Bisection/Small.con" "Bisection__".
-inline "cic:/CoRN/reals/IVT/lft.con".
+inline "cic:/CoRN/reals/IVT/Bisection/lft.con" "Bisection__".
-inline "cic:/CoRN/reals/IVT/rht.con".
+inline "cic:/CoRN/reals/IVT/Bisection/rht.con" "Bisection__".
(* end hide *)
inline "cic:/CoRN/reals/IVT/Cbisect'.con".
(* UNEXPORTED
-End Bisection.
+End Bisection
*)
(* UNEXPORTED
-Section Bisect_Interval.
+Section Bisect_Interval
*)
-inline "cic:/CoRN/reals/IVT/f.var".
+inline "cic:/CoRN/reals/IVT/Bisect_Interval/f.var" "Bisect_Interval__".
-inline "cic:/CoRN/reals/IVT/C_f_apzero_interval.var".
+inline "cic:/CoRN/reals/IVT/Bisect_Interval/C_f_apzero_interval.var" "Bisect_Interval__".
(* begin hide *)
-inline "cic:/CoRN/reals/IVT/Small.con".
+inline "cic:/CoRN/reals/IVT/Bisect_Interval/Small.con" "Bisect_Interval__".
(* end hide *)
inline "cic:/CoRN/reals/IVT/bisect_prop.con".
(* UNEXPORTED
-End Bisect_Interval.
+End Bisect_Interval
*)
(* UNEXPORTED
-Section IVT_Op.
+Section IVT_Op
*)
(*#* ** IVT for operations
Same conventions as before.
*)
-inline "cic:/CoRN/reals/IVT/f.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/f.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/f_contin.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/f_contin.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/f_apzero_interval.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/f_apzero_interval.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/a.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/a.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/b.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/b.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/a_b.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/a_b.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/f_a.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/f_a.var" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/f_b.var".
+inline "cic:/CoRN/reals/IVT/IVT_Op/f_b.var" "IVT_Op__".
(* begin hide *)
-inline "cic:/CoRN/reals/IVT/Small.con".
+inline "cic:/CoRN/reals/IVT/IVT_Op/Small.con" "IVT_Op__".
(* end hide *)
inline "cic:/CoRN/reals/IVT/interval_sequence.con".
-inline "cic:/CoRN/reals/IVT/a_.con".
+inline "cic:/CoRN/reals/IVT/IVT_Op/a_.con" "IVT_Op__".
-inline "cic:/CoRN/reals/IVT/b_.con".
+inline "cic:/CoRN/reals/IVT/IVT_Op/b_.con" "IVT_Op__".
inline "cic:/CoRN/reals/IVT/intervals_smaller.con".
inline "cic:/CoRN/reals/IVT/Civt_op.con".
(* UNEXPORTED
-End IVT_Op.
+End IVT_Op
*)
(* UNEXPORTED
-Section IVT_Poly.
+Section IVT_Poly
*)
(*#* ** IVT for polynomials *)
inline "cic:/CoRN/reals/IVT/Civt_poly.con".
(* UNEXPORTED
-End IVT_Poly.
+End IVT_Poly
*)
include "reals/RealLists.ma".
(* UNEXPORTED
-Section Intervals.
+Section Intervals
*)
(*#* * Intervals
members of the interval [[Min(a,b),Max(a,b)]].
*)
-inline "cic:/CoRN/reals/Intervals/a.var".
+inline "cic:/CoRN/reals/Intervals/Intervals/a.var" "Intervals__".
-inline "cic:/CoRN/reals/Intervals/b.var".
+inline "cic:/CoRN/reals/Intervals/Intervals/b.var" "Intervals__".
-inline "cic:/CoRN/reals/Intervals/Hab.var".
+inline "cic:/CoRN/reals/Intervals/Intervals/Hab.var" "Intervals__".
inline "cic:/CoRN/reals/Intervals/compact_inc_lft.con".
inline "cic:/CoRN/reals/Intervals/Frestr.con".
(* UNEXPORTED
-End Intervals.
+End Intervals
*)
(* NOTATION
*)
(* UNEXPORTED
-Section More_Intervals.
+Section More_Intervals
*)
inline "cic:/CoRN/reals/Intervals/included_refl'.con".
inline "cic:/CoRN/reals/Intervals/compact_map3.con".
(* UNEXPORTED
-End More_Intervals.
+End More_Intervals
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Totally_Bounded.
+Section Totally_Bounded
*)
(*#* ** Totally Bounded
(* begin hide *)
-inline "cic:/CoRN/reals/Intervals/aux_seq_lub.con".
+inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub.con" "Totally_Bounded__".
-inline "cic:/CoRN/reals/Intervals/aux_seq_lub_prop.con".
+inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_lub_prop.con" "Totally_Bounded__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/reals/Intervals/aux_seq_glb.con".
+inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb.con" "Totally_Bounded__".
-inline "cic:/CoRN/reals/Intervals/aux_seq_glb_prop.con".
+inline "cic:/CoRN/reals/Intervals/Totally_Bounded/aux_seq_glb_prop.con" "Totally_Bounded__".
(* end hide *)
inline "cic:/CoRN/reals/Intervals/totally_bounded_has_glb.con".
(* UNEXPORTED
-End Totally_Bounded.
+End Totally_Bounded
*)
(* UNEXPORTED
-Section Compact.
+Section Compact
*)
(*#* ** Compact sets
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Intervals/a.var".
+inline "cic:/CoRN/reals/Intervals/Compact/a.var" "Compact__".
-inline "cic:/CoRN/reals/Intervals/b.var".
+inline "cic:/CoRN/reals/Intervals/Compact/b.var" "Compact__".
-inline "cic:/CoRN/reals/Intervals/Hab.var".
+inline "cic:/CoRN/reals/Intervals/Compact/Hab.var" "Compact__".
(* begin hide *)
-inline "cic:/CoRN/reals/Intervals/I.con".
+inline "cic:/CoRN/reals/Intervals/Compact/I.con" "Compact__".
(* end hide *)
-inline "cic:/CoRN/reals/Intervals/Hab'.var".
+inline "cic:/CoRN/reals/Intervals/Compact/Hab'.var" "Compact__".
-inline "cic:/CoRN/reals/Intervals/e.var".
+inline "cic:/CoRN/reals/Intervals/Compact/e.var" "Compact__".
-inline "cic:/CoRN/reals/Intervals/He.var".
+inline "cic:/CoRN/reals/Intervals/Compact/He.var" "Compact__".
(*#*
We start by finding a natural number [n] such that [(b[-]a) [/] n [<] e].
inline "cic:/CoRN/reals/Intervals/included3_compact.con".
(* UNEXPORTED
-End Compact.
+End Compact
*)
(* UNEXPORTED
include "reals/CauchySeq.ma".
(* UNEXPORTED
-Section Maximum.
+Section Maximum
*)
(* UNEXPORTED
-Section Max_function.
+Section Max_function
*)
(*#* ** Maximum, Minimum and Absolute Value
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Max_AbsIR/x.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/x.var" "Maximum__Max_function__".
-inline "cic:/CoRN/reals/Max_AbsIR/y.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Maximum/Max_function/y.var" "Maximum__Max_function__".
inline "cic:/CoRN/reals/Max_AbsIR/Max_seq.con".
inline "cic:/CoRN/reals/Max_AbsIR/less_MAX_imp.con".
(* UNEXPORTED
-End Max_function.
+End Max_function
*)
inline "cic:/CoRN/reals/Max_AbsIR/MAX_strext.con".
inline "cic:/CoRN/reals/Max_AbsIR/MAX_wd.con".
(* UNEXPORTED
-Section properties_of_Max.
+Section properties_of_Max
*)
(*#* *** Maximum *)
inline "cic:/CoRN/reals/Max_AbsIR/x_div_Max_leEq_x.con".
(* UNEXPORTED
-End properties_of_Max.
+End properties_of_Max
*)
(* UNEXPORTED
-End Maximum.
+End Maximum
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Minimum.
+Section Minimum
*)
(*#* *** Mininum
inline "cic:/CoRN/reals/Max_AbsIR/leEq_Min_plus_eps.con".
-inline "cic:/CoRN/reals/Max_AbsIR/a.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Minimum/a.var" "Minimum__".
-inline "cic:/CoRN/reals/Max_AbsIR/b.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Minimum/b.var" "Minimum__".
inline "cic:/CoRN/reals/Max_AbsIR/Min_leEq_Max.con".
inline "cic:/CoRN/reals/Max_AbsIR/Min_less_Max_imp_ap.con".
(* UNEXPORTED
-End Minimum.
+End Minimum
*)
(*#**********************************)
(* UNEXPORTED
-Section Absolute.
+Section Absolute
*)
(*#**********************************)
inline "cic:/CoRN/reals/Max_AbsIR/AbsIR_bnd.con".
(* UNEXPORTED
-End Absolute.
+End Absolute
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Part_Function_Max.
+Section Part_Function_Max
*)
(*#* *** Functional Operators
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Max_AbsIR/F.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/F.var" "Part_Function_Max__".
-inline "cic:/CoRN/reals/Max_AbsIR/G.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/G.var" "Part_Function_Max__".
(* begin hide *)
-inline "cic:/CoRN/reals/Max_AbsIR/P.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/P.con" "Part_Function_Max__".
-inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Max/Q.con" "Part_Function_Max__".
(* end hide *)
inline "cic:/CoRN/reals/Max_AbsIR/FMax.con".
(* UNEXPORTED
-End Part_Function_Max.
+End Part_Function_Max
*)
(* UNEXPORTED
-Section Part_Function_Abs.
+Section Part_Function_Abs
*)
-inline "cic:/CoRN/reals/Max_AbsIR/F.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/F.var" "Part_Function_Abs__".
-inline "cic:/CoRN/reals/Max_AbsIR/G.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/G.var" "Part_Function_Abs__".
(* begin hide *)
-inline "cic:/CoRN/reals/Max_AbsIR/P.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/P.con" "Part_Function_Abs__".
-inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Part_Function_Abs/Q.con" "Part_Function_Abs__".
(* end hide *)
inline "cic:/CoRN/reals/Max_AbsIR/FAbs_char.con".
(* UNEXPORTED
-End Part_Function_Abs.
+End Part_Function_Abs
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Inclusion.
+Section Inclusion
*)
-inline "cic:/CoRN/reals/Max_AbsIR/F.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/F.var" "Inclusion__".
-inline "cic:/CoRN/reals/Max_AbsIR/G.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/G.var" "Inclusion__".
(* begin hide *)
-inline "cic:/CoRN/reals/Max_AbsIR/P.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/P.con" "Inclusion__".
-inline "cic:/CoRN/reals/Max_AbsIR/Q.con".
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/Q.con" "Inclusion__".
(* end hide *)
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Max_AbsIR/R.var".
+inline "cic:/CoRN/reals/Max_AbsIR/Inclusion/R.var" "Inclusion__".
inline "cic:/CoRN/reals/Max_AbsIR/included_FMax.con".
inline "cic:/CoRN/reals/Max_AbsIR/included_FAbs'.con".
(* UNEXPORTED
-End Inclusion.
+End Inclusion
*)
(* UNEXPORTED
(*#* * Roots of Real Numbers *)
(* UNEXPORTED
-Section NRoot.
+Section NRoot
*)
(*#* ** Existence of roots
%\end{convention}%
*)
-inline "cic:/CoRN/reals/NRootIR/n.var".
+inline "cic:/CoRN/reals/NRootIR/NRoot/n.var" "NRoot__".
-inline "cic:/CoRN/reals/NRootIR/n_pos.var".
+inline "cic:/CoRN/reals/NRootIR/NRoot/n_pos.var" "NRoot__".
-inline "cic:/CoRN/reals/NRootIR/c.var".
+inline "cic:/CoRN/reals/NRootIR/NRoot/c.var" "NRoot__".
-inline "cic:/CoRN/reals/NRootIR/c_nonneg.var".
+inline "cic:/CoRN/reals/NRootIR/NRoot/c_nonneg.var" "NRoot__".
(* begin hide *)
-inline "cic:/CoRN/reals/NRootIR/p.con".
+inline "cic:/CoRN/reals/NRootIR/NRoot/p.con" "NRoot__".
(* end hide *)
inline "cic:/CoRN/reals/NRootIR/CnrootIR.con".
(* UNEXPORTED
-End NRoot.
+End NRoot
*)
(*#* We define the root of order [n] for any nonnegative real number and
*)
(* UNEXPORTED
-Section Nth_Root.
+Section Nth_Root
*)
inline "cic:/CoRN/reals/NRootIR/nroot.con".
(*#* %\begin{convention}% Let [x,y] be nonnegative real numbers.
%\end{convention}% *)
-inline "cic:/CoRN/reals/NRootIR/x.var".
+inline "cic:/CoRN/reals/NRootIR/Nth_Root/x.var" "Nth_Root__".
-inline "cic:/CoRN/reals/NRootIR/y.var".
+inline "cic:/CoRN/reals/NRootIR/Nth_Root/y.var" "Nth_Root__".
-inline "cic:/CoRN/reals/NRootIR/Hx.var".
+inline "cic:/CoRN/reals/NRootIR/Nth_Root/Hx.var" "Nth_Root__".
-inline "cic:/CoRN/reals/NRootIR/Hy.var".
+inline "cic:/CoRN/reals/NRootIR/Nth_Root/Hy.var" "Nth_Root__".
inline "cic:/CoRN/reals/NRootIR/NRoot_wd.con".
inline "cic:/CoRN/reals/NRootIR/NRoot_unique.con".
(* UNEXPORTED
-End Nth_Root.
+End Nth_Root
*)
(* UNEXPORTED
(*#**********************************)
(* UNEXPORTED
-Section Square_root.
+Section Square_root
*)
(*#**********************************)
inline "cic:/CoRN/reals/NRootIR/sqrt_resp_less.con".
(* UNEXPORTED
-End Square_root.
+End Square_root
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Absolute_Props.
+Section Absolute_Props
*)
(*#* ** More on absolute value
inline "cic:/CoRN/reals/NRootIR/AbsIR_bnd_AbsIR.con".
(* UNEXPORTED
-End Absolute_Props.
+End Absolute_Props
*)
(* UNEXPORTED
-Section Consequences.
+Section Consequences
*)
(*#* **Cauchy sequences
inline "cic:/CoRN/reals/NRootIR/Lim_recip.con".
(* UNEXPORTED
-End Consequences.
+End Consequences
*)
(*#* * Roots of polynomials of odd degree *)
(* UNEXPORTED
-Section CPoly_Big.
+Section CPoly_Big
*)
(*#* ** Monic polynomials are positive near infinity
%\end{convention}%
*)
-inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
+inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/R.var" "CPoly_Big__".
(* begin hide *)
-inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
+inline "cic:/CoRN/reals/OddPolyRootIR/CPoly_Big/RX.con" "CPoly_Big__".
(* end hide *)
inline "cic:/CoRN/reals/OddPolyRootIR/Ccpoly_pos'.con".
(* UNEXPORTED
-End CPoly_Big.
+End CPoly_Big
*)
(* UNEXPORTED
-Section Flip_Poly.
+Section Flip_Poly
*)
(*#* **Flipping a polynomial
%\end{convention}%
*)
-inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
+inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/R.var" "Flip_Poly__".
(* begin hide *)
-inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
+inline "cic:/CoRN/reals/OddPolyRootIR/Flip_Poly/RX.con" "Flip_Poly__".
(* end hide *)
inline "cic:/CoRN/reals/OddPolyRootIR/flip_odd.con".
(* UNEXPORTED
-End Flip_Poly.
+End Flip_Poly
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section OddPoly_Signs.
+Section OddPoly_Signs
*)
(*#* ** Sign of a polynomial of odd degree
%\end{convention}%
*)
-inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
+inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/R.var" "OddPoly_Signs__".
(* begin hide *)
-inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
+inline "cic:/CoRN/reals/OddPolyRootIR/OddPoly_Signs/RX.con" "OddPoly_Signs__".
(* end hide *)
inline "cic:/CoRN/reals/OddPolyRootIR/oddpoly_neg.con".
(* UNEXPORTED
-End OddPoly_Signs.
+End OddPoly_Signs
*)
(* UNEXPORTED
-Section Poly_Norm.
+Section Poly_Norm
*)
(*#* ** The norm of a polynomial
%\end{convention}%
*)
-inline "cic:/CoRN/reals/OddPolyRootIR/R.var".
+inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/R.var" "Poly_Norm__".
(* begin hide *)
-inline "cic:/CoRN/reals/OddPolyRootIR/RX.con".
+inline "cic:/CoRN/reals/OddPolyRootIR/Poly_Norm/RX.con" "Poly_Norm__".
(* end hide *)
inline "cic:/CoRN/reals/OddPolyRootIR/poly_norm_apply.con".
(* UNEXPORTED
-End Poly_Norm.
+End Poly_Norm
*)
(* UNEXPORTED
-Section OddPoly_Root.
+Section OddPoly_Root
*)
(*#* ** Roots of polynomials of odd degree
inline "cic:/CoRN/reals/OddPolyRootIR/realpolyn_oddhaszero.con".
(* UNEXPORTED
-End OddPoly_Root.
+End OddPoly_Root
*)
inline "cic:/CoRN/reals/Q_dense/or_not_and.con".
(* UNEXPORTED
-Section Interval_definition.
+Section Interval_definition
*)
-inline "cic:/CoRN/reals/Q_dense/OF.var".
+inline "cic:/CoRN/reals/Q_dense/Interval_definition/OF.var" "Interval_definition__".
inline "cic:/CoRN/reals/Q_dense/Interval.ind".
inline "cic:/CoRN/reals/Q_dense/Length.con".
(* UNEXPORTED
-End Interval_definition.
+End Interval_definition
*)
inline "cic:/CoRN/reals/Q_dense/Rat_Interval.con".
*)
(* UNEXPORTED
-Section COrdField_extra.
+Section COrdField_extra
*)
-inline "cic:/CoRN/reals/Q_dense/OF.var".
+inline "cic:/CoRN/reals/Q_dense/COrdField_extra/OF.var" "COrdField_extra__".
inline "cic:/CoRN/reals/Q_dense/AbsSmall_pos_reflexive.con".
inline "cic:/CoRN/reals/Q_dense/AbsSmall_subinterval.con".
(* UNEXPORTED
-End COrdField_extra.
+End COrdField_extra
*)
(* UNEXPORTED
-Section Rational_sequence.
+Section Rational_sequence
*)
include "tactics/Opaque_algebra.ma".
(*#*** WARNING: A file is being loaded *****)
-inline "cic:/CoRN/reals/Q_dense/R1.var".
+inline "cic:/CoRN/reals/Q_dense/Rational_sequence/R1.var" "Rational_sequence__".
inline "cic:/CoRN/reals/Q_dense/start_l.con".
inline "cic:/CoRN/reals/Q_dense/x_is_SeqLimit_G.con".
(* UNEXPORTED
-End Rational_sequence.
+End Rational_sequence
*)
(* end hide *)
include "model/rings/Zring.ma".
(* UNEXPORTED
-Section Rational_sequence_prelogue.
+Section Rational_sequence_prelogue
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Q_in_CReals/R1.var".
+inline "cic:/CoRN/reals/Q_in_CReals/Rational_sequence_prelogue/R1.var" "Rational_sequence_prelogue__".
(* We clone these proofs from CReals1.v just because there IR is an axiom *)
inline "cic:/CoRN/reals/Q_in_CReals/Q_dense_in_CReals.con".
(* UNEXPORTED
-End Rational_sequence_prelogue.
+End Rational_sequence_prelogue
*)
inline "cic:/CoRN/reals/R_morphism/Cauchy_Lim_prop2.con".
(* UNEXPORTED
-Section morphism.
+Section morphism
*)
-inline "cic:/CoRN/reals/R_morphism/R1.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/R1.var" "morphism__".
-inline "cic:/CoRN/reals/R_morphism/R2.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/R2.var" "morphism__".
(* UNEXPORTED
-Section morphism_details.
+Section morphism_details
*)
-inline "cic:/CoRN/reals/R_morphism/phi.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/phi.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/p1.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p1.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/p2.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/p2.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/f1.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f1.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/f2.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/f2.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/g1.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g1.var" "morphism__morphism_details__".
-inline "cic:/CoRN/reals/R_morphism/g2.var".
+inline "cic:/CoRN/reals/R_morphism/morphism/morphism_details/g2.var" "morphism__morphism_details__".
inline "cic:/CoRN/reals/R_morphism/fun_pres_relation.con".
inline "cic:/CoRN/reals/R_morphism/fun_pres_Lim.con".
(* UNEXPORTED
-End morphism_details.
+End morphism_details
*)
inline "cic:/CoRN/reals/R_morphism/Homomorphism.ind".
inline "cic:/CoRN/reals/R_morphism/map_pres_inv_unfolded.con".
(* UNEXPORTED
-End morphism.
+End morphism
*)
(* UNEXPORTED
-Section composition.
+Section composition
*)
-inline "cic:/CoRN/reals/R_morphism/R1.var".
+inline "cic:/CoRN/reals/R_morphism/composition/R1.var" "composition__".
-inline "cic:/CoRN/reals/R_morphism/R2.var".
+inline "cic:/CoRN/reals/R_morphism/composition/R2.var" "composition__".
-inline "cic:/CoRN/reals/R_morphism/R3.var".
+inline "cic:/CoRN/reals/R_morphism/composition/R3.var" "composition__".
-inline "cic:/CoRN/reals/R_morphism/f.var".
+inline "cic:/CoRN/reals/R_morphism/composition/f.var" "composition__".
-inline "cic:/CoRN/reals/R_morphism/g.var".
+inline "cic:/CoRN/reals/R_morphism/composition/g.var" "composition__".
inline "cic:/CoRN/reals/R_morphism/compose.con".
inline "cic:/CoRN/reals/R_morphism/Compose.con".
(* UNEXPORTED
-End composition.
+End composition
*)
(* UNEXPORTED
-Section isomorphism.
+Section isomorphism
*)
-inline "cic:/CoRN/reals/R_morphism/R1.var".
+inline "cic:/CoRN/reals/R_morphism/isomorphism/R1.var" "isomorphism__".
-inline "cic:/CoRN/reals/R_morphism/R2.var".
+inline "cic:/CoRN/reals/R_morphism/isomorphism/R2.var" "isomorphism__".
(* UNEXPORTED
-Section identity_map.
+Section identity_map
*)
-inline "cic:/CoRN/reals/R_morphism/R3.var".
+inline "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/R3.var" "isomorphism__identity_map__".
-inline "cic:/CoRN/reals/R_morphism/f.var".
+inline "cic:/CoRN/reals/R_morphism/isomorphism/identity_map/f.var" "isomorphism__identity_map__".
inline "cic:/CoRN/reals/R_morphism/map_is_id.con".
(* UNEXPORTED
-End identity_map.
+End identity_map
*)
inline "cic:/CoRN/reals/R_morphism/Isomorphism.ind".
(* UNEXPORTED
-End isomorphism.
+End isomorphism
*)
(* UNEXPORTED
-Section surjective_map.
+Section surjective_map
*)
-inline "cic:/CoRN/reals/R_morphism/R1.var".
+inline "cic:/CoRN/reals/R_morphism/surjective_map/R1.var" "surjective_map__".
-inline "cic:/CoRN/reals/R_morphism/R2.var".
+inline "cic:/CoRN/reals/R_morphism/surjective_map/R2.var" "surjective_map__".
-inline "cic:/CoRN/reals/R_morphism/f.var".
+inline "cic:/CoRN/reals/R_morphism/surjective_map/f.var" "surjective_map__".
inline "cic:/CoRN/reals/R_morphism/map_is_surjective.con".
(* UNEXPORTED
-End surjective_map.
+End surjective_map
*)
(* UNEXPORTED
-Section simplification.
+Section simplification
*)
-inline "cic:/CoRN/reals/R_morphism/R1.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/R1.var" "simplification__".
-inline "cic:/CoRN/reals/R_morphism/R2.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/R2.var" "simplification__".
-inline "cic:/CoRN/reals/R_morphism/f.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/f.var" "simplification__".
-inline "cic:/CoRN/reals/R_morphism/H1.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/H1.var" "simplification__".
inline "cic:/CoRN/reals/R_morphism/f_well_def.con".
(* UNEXPORTED
-Section with_less.
+Section with_less
*)
-inline "cic:/CoRN/reals/R_morphism/H2.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_less/H2.var" "simplification__with_less__".
inline "cic:/CoRN/reals/R_morphism/less_pres_f.con".
inline "cic:/CoRN/reals/R_morphism/f_pres_apartness.con".
(* UNEXPORTED
-End with_less.
+End with_less
*)
(* UNEXPORTED
-Section with_plus.
+Section with_plus
*)
-inline "cic:/CoRN/reals/R_morphism/H3.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_plus/H3.var" "simplification__with_plus__".
inline "cic:/CoRN/reals/R_morphism/f_pres_Zero.con".
inline "cic:/CoRN/reals/R_morphism/f_pres_min.con".
(* UNEXPORTED
-End with_plus.
+End with_plus
*)
(* UNEXPORTED
-Section with_plus_less.
+Section with_plus_less
*)
-inline "cic:/CoRN/reals/R_morphism/H2.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H2.var" "simplification__with_plus_less__".
-inline "cic:/CoRN/reals/R_morphism/H3.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/H3.var" "simplification__with_plus_less__".
inline "cic:/CoRN/reals/R_morphism/f_pres_ap_zero.con".
(* UNEXPORTED
-Section surjectivity_helps.
+Section surjectivity_helps
*)
-inline "cic:/CoRN/reals/R_morphism/f_surj.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/surjectivity_helps/f_surj.var" "simplification__with_plus_less__surjectivity_helps__".
inline "cic:/CoRN/reals/R_morphism/f_pres_Lim.con".
(* UNEXPORTED
-End surjectivity_helps.
+End surjectivity_helps
*)
(* UNEXPORTED
-Section with_mult_plus_less.
+Section with_mult_plus_less
*)
-inline "cic:/CoRN/reals/R_morphism/H4.var".
+inline "cic:/CoRN/reals/R_morphism/simplification/with_plus_less/with_mult_plus_less/H4.var" "simplification__with_plus_less__with_mult_plus_less__".
inline "cic:/CoRN/reals/R_morphism/f_pres_one.con".
inline "cic:/CoRN/reals/R_morphism/simplified_Homomorphism.con".
(* UNEXPORTED
-End with_mult_plus_less.
+End with_mult_plus_less
*)
(* UNEXPORTED
-End with_plus_less.
+End with_plus_less
*)
(* UNEXPORTED
-End simplification.
+End simplification
*)
(* end hide *)
(* end hide *)
(* UNEXPORTED
-Section Continuity.
+Section Continuity
*)
-inline "cic:/CoRN/reals/RealFuncts/f.var".
+inline "cic:/CoRN/reals/RealFuncts/Continuity/f.var" "Continuity__".
-inline "cic:/CoRN/reals/RealFuncts/f2.var".
+inline "cic:/CoRN/reals/RealFuncts/Continuity/f2.var" "Continuity__".
(*#*
Let [f] be a unary setoid operation on [IR] and
*)
(* UNEXPORTED
-End Continuity.
+End Continuity
*)
(* begin hide *)
include "reals/CReals1.ma".
(* UNEXPORTED
-Section Lists.
+Section Lists
*)
(*#* * Lists of Real Numbers
(* begin hide *)
-inline "cic:/CoRN/reals/RealLists/maxlist_aux.con".
+inline "cic:/CoRN/reals/RealLists/Lists/maxlist_aux.con" "Lists__".
(* end hide *)
(* begin hide *)
-inline "cic:/CoRN/reals/RealLists/minlist_aux.con".
+inline "cic:/CoRN/reals/RealLists/Lists/minlist_aux.con" "Lists__".
(* end hide *)
inline "cic:/CoRN/reals/RealLists/leEq_minlist.con".
(* UNEXPORTED
-End Lists.
+End Lists
*)
include "reals/NRootIR.ma".
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* *Series of Real Numbers
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Definitions/x.var" "Definitions__".
inline "cic:/CoRN/reals/Series/seq_part_sum.con".
inline "cic:/CoRN/reals/Series/series_seq_Lim'.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section More_Definitions.
+Section More_Definitions
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/More_Definitions/x.var" "More_Definitions__".
(*#* We also define absolute convergence. *)
inline "cic:/CoRN/reals/Series/abs_convergent.con".
(* UNEXPORTED
-End More_Definitions.
+End More_Definitions
*)
(* UNEXPORTED
-Section Power_Series.
+Section Power_Series
*)
(*#* **Power Series
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Series/c.var".
+inline "cic:/CoRN/reals/Series/Power_Series/c.var" "Power_Series__".
-inline "cic:/CoRN/reals/Series/H0c.var".
+inline "cic:/CoRN/reals/Series/Power_Series/H0c.var" "Power_Series__".
-inline "cic:/CoRN/reals/Series/Hc1.var".
+inline "cic:/CoRN/reals/Series/Power_Series/Hc1.var" "Power_Series__".
inline "cic:/CoRN/reals/Series/c_exp_Lim.con".
inline "cic:/CoRN/reals/Series/power_series_sum.con".
(* UNEXPORTED
-End Power_Series.
+End Power_Series
*)
(* UNEXPORTED
-Section Operations.
+Section Operations
*)
(*#* **Operations
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Operations/x.var" "Operations__".
-inline "cic:/CoRN/reals/Series/y.var".
+inline "cic:/CoRN/reals/Series/Operations/y.var" "Operations__".
-inline "cic:/CoRN/reals/Series/convX.var".
+inline "cic:/CoRN/reals/Series/Operations/convX.var" "Operations__".
-inline "cic:/CoRN/reals/Series/convY.var".
+inline "cic:/CoRN/reals/Series/Operations/convY.var" "Operations__".
inline "cic:/CoRN/reals/Series/convergent_wd.con".
(*#* Multiplication by a scalar [c] is also permitted. *)
-inline "cic:/CoRN/reals/Series/c.var".
+inline "cic:/CoRN/reals/Series/Operations/c.var" "Operations__".
inline "cic:/CoRN/reals/Series/conv_series_mult_scal.con".
inline "cic:/CoRN/reals/Series/series_sum_mult_scal.con".
(* UNEXPORTED
-End Operations.
+End Operations
*)
(* UNEXPORTED
-Section More_Operations.
+Section More_Operations
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/More_Operations/x.var" "More_Operations__".
-inline "cic:/CoRN/reals/Series/convX.var".
+inline "cic:/CoRN/reals/Series/More_Operations/convX.var" "More_Operations__".
(*#* As a corollary, we get the series of the inverses. *)
inline "cic:/CoRN/reals/Series/series_sum_inv.con".
(* UNEXPORTED
-End More_Operations.
+End More_Operations
*)
(* UNEXPORTED
-Section Almost_Everywhere.
+Section Almost_Everywhere
*)
(*#* ** Almost Everywhere
Let [x,y : nat->IR] be equal after some natural number.
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Almost_Everywhere/x.var" "Almost_Everywhere__".
-inline "cic:/CoRN/reals/Series/y.var".
+inline "cic:/CoRN/reals/Series/Almost_Everywhere/y.var" "Almost_Everywhere__".
inline "cic:/CoRN/reals/Series/aew_eq.con".
-inline "cic:/CoRN/reals/Series/aew_equal.var".
+inline "cic:/CoRN/reals/Series/Almost_Everywhere/aew_equal.var" "Almost_Everywhere__".
inline "cic:/CoRN/reals/Series/aew_Cauchy.con".
inline "cic:/CoRN/reals/Series/aew_series_conv.con".
(* UNEXPORTED
-End Almost_Everywhere.
+End Almost_Everywhere
*)
(* UNEXPORTED
-Section Cauchy_Almost_Everywhere.
+Section Cauchy_Almost_Everywhere
*)
(*#* Suppose furthermore that [x,y] are Cauchy sequences. *)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/x.var" "Cauchy_Almost_Everywhere__".
-inline "cic:/CoRN/reals/Series/y.var".
+inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/y.var" "Cauchy_Almost_Everywhere__".
-inline "cic:/CoRN/reals/Series/aew_equal.var".
+inline "cic:/CoRN/reals/Series/Cauchy_Almost_Everywhere/aew_equal.var" "Cauchy_Almost_Everywhere__".
inline "cic:/CoRN/reals/Series/aew_Lim.con".
(* UNEXPORTED
-End Cauchy_Almost_Everywhere.
+End Cauchy_Almost_Everywhere
*)
(* UNEXPORTED
-Section Convergence_Criteria.
+Section Convergence_Criteria
*)
(*#* **Convergence Criteria
%\end{convention}%
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Convergence_Criteria/x.var" "Convergence_Criteria__".
(*#* We include the comparison test for series, both in a strong and in a less
general (but simpler) form.
inline "cic:/CoRN/reals/Series/join_series.con".
(* UNEXPORTED
-End Convergence_Criteria.
+End Convergence_Criteria
*)
(* UNEXPORTED
-Section More_CC.
+Section More_CC
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/More_CC/x.var" "More_CC__".
inline "cic:/CoRN/reals/Series/ratio_test_conv.con".
inline "cic:/CoRN/reals/Series/ratio_test_div.con".
(* UNEXPORTED
-End More_CC.
+End More_CC
*)
(* UNEXPORTED
-Section Alternate_Series.
+Section Alternate_Series
*)
(*#* **Alternate Series
decreasing convergent to 0.
*)
-inline "cic:/CoRN/reals/Series/x.var".
+inline "cic:/CoRN/reals/Series/Alternate_Series/x.var" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/pos_x.var".
+inline "cic:/CoRN/reals/Series/Alternate_Series/pos_x.var" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/Lim_x.var".
+inline "cic:/CoRN/reals/Series/Alternate_Series/Lim_x.var" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/mon_x.var".
+inline "cic:/CoRN/reals/Series/Alternate_Series/mon_x.var" "Alternate_Series__".
(* begin hide *)
-inline "cic:/CoRN/reals/Series/y.con".
+inline "cic:/CoRN/reals/Series/Alternate_Series/y.con" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/alternate_lemma1.con".
+inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma1.con" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/alternate_lemma2.con".
+inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma2.con" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/alternate_lemma3.con".
+inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma3.con" "Alternate_Series__".
-inline "cic:/CoRN/reals/Series/alternate_lemma4.con".
+inline "cic:/CoRN/reals/Series/Alternate_Series/alternate_lemma4.con" "Alternate_Series__".
(* end hide *)
inline "cic:/CoRN/reals/Series/alternate_series_conv.con".
(* UNEXPORTED
-End Alternate_Series.
+End Alternate_Series
*)
(* UNEXPORTED
-Section Important_Numbers.
+Section Important_Numbers
*)
(*#* **Important Numbers
inline "cic:/CoRN/reals/Series/pi.con".
(* UNEXPORTED
-End Important_Numbers.
+End Important_Numbers
*)
inline "cic:/CoRN/reals/iso_CReals/G_pres_mult.con".
(* UNEXPORTED
-Section Concrete_iso_between_Creals.
+Section Concrete_iso_between_Creals
*)
-inline "cic:/CoRN/reals/iso_CReals/R1.var".
+inline "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R1.var" "Concrete_iso_between_Creals__".
-inline "cic:/CoRN/reals/iso_CReals/R2.var".
+inline "cic:/CoRN/reals/iso_CReals/Concrete_iso_between_Creals/R2.var" "Concrete_iso_between_Creals__".
inline "cic:/CoRN/reals/iso_CReals/image_Cauchy12.con".
inline "cic:/CoRN/reals/iso_CReals/Canonic_Isomorphism_between_CReals.con".
(* UNEXPORTED
-End Concrete_iso_between_Creals.
+End Concrete_iso_between_Creals
*)
(* end hide *)
include "algebra/CLogic.ma".
(* UNEXPORTED
-Section Syntactic_Expressions.
+Section Syntactic_Expressions
*)
inline "cic:/CoRN/tactics/AlgReflection/varindex.con".
inline "cic:/CoRN/tactics/AlgReflection/expr_power.con".
(* UNEXPORTED
-End Syntactic_Expressions.
+End Syntactic_Expressions
*)
(* UNEXPORTED
-Section Normalization_Function.
+Section Normalization_Function
*)
inline "cic:/CoRN/tactics/AlgReflection/eq_nat.con".
inline "cic:/CoRN/tactics/AlgReflection/expr_is_zero.con".
(* UNEXPORTED
-End Normalization_Function.
+End Normalization_Function
*)
(* UNEXPORTED
-Section Correctness_Results.
+Section Correctness_Results
*)
inline "cic:/CoRN/tactics/AlgReflection/eq_nat_corr.con".
inline "cic:/CoRN/tactics/AlgReflection/eq_expr_corr.con".
(* UNEXPORTED
-End Correctness_Results.
+End Correctness_Results
*)
(* end hide *)
include "ftc/Differentiability.ma".
(* UNEXPORTED
-Section Automatizing_Continuity.
+Section Automatizing_Continuity
*)
-inline "cic:/CoRN/tactics/DiffTactics2/a.var".
+inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/a.var" "Automatizing_Continuity__".
-inline "cic:/CoRN/tactics/DiffTactics2/b.var".
+inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Continuity/b.var" "Automatizing_Continuity__".
inline "cic:/CoRN/tactics/DiffTactics2/cont_function.ind".
inline "cic:/CoRN/tactics/DiffTactics2/continuous_cont.con".
(* UNEXPORTED
-End Automatizing_Continuity.
+End Automatizing_Continuity
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Automatizing_Derivatives.
+Section Automatizing_Derivatives
*)
-inline "cic:/CoRN/tactics/DiffTactics2/a.var".
+inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/a.var" "Automatizing_Derivatives__".
-inline "cic:/CoRN/tactics/DiffTactics2/b.var".
+inline "cic:/CoRN/tactics/DiffTactics2/Automatizing_Derivatives/b.var" "Automatizing_Derivatives__".
inline "cic:/CoRN/tactics/DiffTactics2/deriv_function.ind".
inline "cic:/CoRN/tactics/DiffTactics2/diffble_restr.con".
(* UNEXPORTED
-End Automatizing_Derivatives.
+End Automatizing_Derivatives
*)
(* UNEXPORTED
include "tactics/AlgReflection.ma".
(* UNEXPORTED
-Section Field_Interpretation_Function.
+Section Field_Interpretation_Function
*)
-inline "cic:/CoRN/tactics/FieldReflection/F.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/F.var" "Field_Interpretation_Function__".
-inline "cic:/CoRN/tactics/FieldReflection/val.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/val.var" "Field_Interpretation_Function__".
-inline "cic:/CoRN/tactics/FieldReflection/unop.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/unop.var" "Field_Interpretation_Function__".
-inline "cic:/CoRN/tactics/FieldReflection/binop.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/binop.var" "Field_Interpretation_Function__".
-inline "cic:/CoRN/tactics/FieldReflection/pfun.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_Interpretation_Function/pfun.var" "Field_Interpretation_Function__".
inline "cic:/CoRN/tactics/FieldReflection/interpF.ind".
inline "cic:/CoRN/tactics/FieldReflection/interpF_wd.con".
(* UNEXPORTED
-End Field_Interpretation_Function.
+End Field_Interpretation_Function
*)
(* UNEXPORTED
-Section Field_NormCorrect.
+Section Field_NormCorrect
*)
-inline "cic:/CoRN/tactics/FieldReflection/F.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/F.var" "Field_NormCorrect__".
-inline "cic:/CoRN/tactics/FieldReflection/val.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/val.var" "Field_NormCorrect__".
-inline "cic:/CoRN/tactics/FieldReflection/unop.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/unop.var" "Field_NormCorrect__".
-inline "cic:/CoRN/tactics/FieldReflection/binop.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/binop.var" "Field_NormCorrect__".
-inline "cic:/CoRN/tactics/FieldReflection/pfun.var".
+inline "cic:/CoRN/tactics/FieldReflection/Field_NormCorrect/pfun.var" "Field_NormCorrect__".
(* NOTATION
Notation II := (interpF F val unop binop pfun).
inline "cic:/CoRN/tactics/FieldReflection/Tactic_lemmaF.con".
(* UNEXPORTED
-End Field_NormCorrect.
+End Field_NormCorrect
*)
(* end hide *)
include "tactics/AlgReflection.ma".
(* UNEXPORTED
-Section Group_Interpretation_Function.
+Section Group_Interpretation_Function
*)
-inline "cic:/CoRN/tactics/GroupReflection/G.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/G.var" "Group_Interpretation_Function__".
-inline "cic:/CoRN/tactics/GroupReflection/val.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/val.var" "Group_Interpretation_Function__".
-inline "cic:/CoRN/tactics/GroupReflection/unop.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/unop.var" "Group_Interpretation_Function__".
-inline "cic:/CoRN/tactics/GroupReflection/binop.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/binop.var" "Group_Interpretation_Function__".
-inline "cic:/CoRN/tactics/GroupReflection/pfun.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_Interpretation_Function/pfun.var" "Group_Interpretation_Function__".
inline "cic:/CoRN/tactics/GroupReflection/interpG.ind".
inline "cic:/CoRN/tactics/GroupReflection/interpG_wd.con".
(* UNEXPORTED
-End Group_Interpretation_Function.
+End Group_Interpretation_Function
*)
(* UNEXPORTED
-Section Group_NormCorrect.
+Section Group_NormCorrect
*)
-inline "cic:/CoRN/tactics/GroupReflection/G.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/G.var" "Group_NormCorrect__".
-inline "cic:/CoRN/tactics/GroupReflection/val.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/val.var" "Group_NormCorrect__".
-inline "cic:/CoRN/tactics/GroupReflection/unop.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/unop.var" "Group_NormCorrect__".
-inline "cic:/CoRN/tactics/GroupReflection/binop.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/binop.var" "Group_NormCorrect__".
-inline "cic:/CoRN/tactics/GroupReflection/pfun.var".
+inline "cic:/CoRN/tactics/GroupReflection/Group_NormCorrect/pfun.var" "Group_NormCorrect__".
(* NOTATION
Notation II := (interpG G val unop binop pfun).
inline "cic:/CoRN/tactics/GroupReflection/Tactic_lemmaG.con".
(* UNEXPORTED
-End Group_NormCorrect.
+End Group_NormCorrect
*)
(* end hide *)
include "tactics/AlgReflection.ma".
(* UNEXPORTED
-Section Ring_Interpretation_Function.
+Section Ring_Interpretation_Function
*)
-inline "cic:/CoRN/tactics/RingReflection/R.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/R.var" "Ring_Interpretation_Function__".
-inline "cic:/CoRN/tactics/RingReflection/val.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/val.var" "Ring_Interpretation_Function__".
-inline "cic:/CoRN/tactics/RingReflection/unop.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/unop.var" "Ring_Interpretation_Function__".
-inline "cic:/CoRN/tactics/RingReflection/binop.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/binop.var" "Ring_Interpretation_Function__".
-inline "cic:/CoRN/tactics/RingReflection/pfun.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_Interpretation_Function/pfun.var" "Ring_Interpretation_Function__".
inline "cic:/CoRN/tactics/RingReflection/interpR.ind".
inline "cic:/CoRN/tactics/RingReflection/interpR_wd.con".
(* UNEXPORTED
-End Ring_Interpretation_Function.
+End Ring_Interpretation_Function
*)
(* UNEXPORTED
-Section Ring_NormCorrect.
+Section Ring_NormCorrect
*)
-inline "cic:/CoRN/tactics/RingReflection/R.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/R.var" "Ring_NormCorrect__".
-inline "cic:/CoRN/tactics/RingReflection/val.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/val.var" "Ring_NormCorrect__".
-inline "cic:/CoRN/tactics/RingReflection/unop.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/unop.var" "Ring_NormCorrect__".
-inline "cic:/CoRN/tactics/RingReflection/binop.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/binop.var" "Ring_NormCorrect__".
-inline "cic:/CoRN/tactics/RingReflection/pfun.var".
+inline "cic:/CoRN/tactics/RingReflection/Ring_NormCorrect/pfun.var" "Ring_NormCorrect__".
(* NOTATION
Notation II := (interpR R val unop binop pfun).
inline "cic:/CoRN/tactics/RingReflection/Tactic_lemmaR.con".
(* UNEXPORTED
-End Ring_NormCorrect.
+End Ring_NormCorrect
*)
(* end hide *)
*)
(* UNEXPORTED
-Section Inverses.
+Section Inverses
*)
(*#* **Composition properties
*)
(* UNEXPORTED
-Section ArcTan_Range.
+Section ArcTan_Range
*)
-inline "cic:/CoRN/transc/InvTrigonom/x.var".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/x.var" "Inverses__ArcTan_Range__".
(* begin hide *)
-inline "cic:/CoRN/transc/InvTrigonom/min.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min1.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min1.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min2.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min2.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min3.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min3.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min4.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min4.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max1.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max1.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max2.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max2.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max3.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max3.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max4.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max4.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min5.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min5.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/min6.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/min6.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max5.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max5.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/max6.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/max6.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a1.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a1.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a2.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a2.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a3.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a3.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a4.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a4.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/a5.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/a5.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b1.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b1.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b2.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b2.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b3.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b3.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b4.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b4.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/b5.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/b5.con" "Inverses__ArcTan_Range__".
-inline "cic:/CoRN/transc/InvTrigonom/ab.con".
+inline "cic:/CoRN/transc/InvTrigonom/Inverses/ArcTan_Range/ab.con" "Inverses__ArcTan_Range__".
inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range_lemma.con".
inline "cic:/CoRN/transc/InvTrigonom/ArcTan_range.con".
(* UNEXPORTED
-End ArcTan_Range.
+End ArcTan_Range
*)
(* UNEXPORTED
inline "cic:/CoRN/transc/InvTrigonom/Tan_ArcTan_inv.con".
(* UNEXPORTED
-End Inverses.
+End Inverses
*)
include "transc/SinCos.ma".
(* UNEXPORTED
-Section Properties_of_Pi.
+Section Properties_of_Pi
*)
(*#* printing Pi %\ensuremath{\pi}% #π# *)
inline "cic:/CoRN/transc/Pi/pos_Pi.con".
(* UNEXPORTED
-End Properties_of_Pi.
+End Properties_of_Pi
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Pi_and_Order.
+Section Pi_and_Order
*)
(*#* **Properties of Pi
inline "cic:/CoRN/transc/Pi/invQuarterPi_less_QuarterPi.con".
(* UNEXPORTED
-End Pi_and_Order.
+End Pi_and_Order
*)
(* UNEXPORTED
(* end hide *)
(* UNEXPORTED
-Section Sin_And_Cos.
+Section Sin_And_Cos
*)
(*#* **More formulas
inline "cic:/CoRN/transc/Pi/Tan_periodic.con".
(* UNEXPORTED
-End Sin_And_Cos.
+End Sin_And_Cos
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Power_Series.
+Section Power_Series
*)
(*#* **General results
%\end{convention}%
*)
-inline "cic:/CoRN/transc/PowerSeries/J.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/J.var" "Power_Series__".
-inline "cic:/CoRN/transc/PowerSeries/x0.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/x0.var" "Power_Series__".
-inline "cic:/CoRN/transc/PowerSeries/Hx0.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/Hx0.var" "Power_Series__".
-inline "cic:/CoRN/transc/PowerSeries/a.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/a.var" "Power_Series__".
inline "cic:/CoRN/transc/PowerSeries/FPowerSeries.con".
(* begin show *)
-inline "cic:/CoRN/transc/PowerSeries/Ha.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/Ha.var" "Power_Series__".
-inline "cic:/CoRN/transc/PowerSeries/r.con".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/r.con" "Power_Series__".
-inline "cic:/CoRN/transc/PowerSeries/Hr.con".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/Hr.con" "Power_Series__".
(* end show *)
(* begin show *)
-inline "cic:/CoRN/transc/PowerSeries/Ha'.var".
+inline "cic:/CoRN/transc/PowerSeries/Power_Series/Ha'.var" "Power_Series__".
(* end show *)
inline "cic:/CoRN/transc/PowerSeries/FPowerSeries'_conv.con".
(* UNEXPORTED
-End Power_Series.
+End Power_Series
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section More_on_PowerSeries.
+Section More_on_PowerSeries
*)
(*#*
%\end{convention}%
*)
-inline "cic:/CoRN/transc/PowerSeries/x0.var".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/x0.var" "More_on_PowerSeries__".
-inline "cic:/CoRN/transc/PowerSeries/a.var".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/a.var" "More_on_PowerSeries__".
(* begin hide *)
-inline "cic:/CoRN/transc/PowerSeries/F.con".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/F.con" "More_on_PowerSeries__".
-inline "cic:/CoRN/transc/PowerSeries/G.con".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/G.con" "More_on_PowerSeries__".
(* end hide *)
(* begin show *)
-inline "cic:/CoRN/transc/PowerSeries/Hf.var".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf.var" "More_on_PowerSeries__".
-inline "cic:/CoRN/transc/PowerSeries/Hf'.var".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hf'.var" "More_on_PowerSeries__".
-inline "cic:/CoRN/transc/PowerSeries/Hg.var".
+inline "cic:/CoRN/transc/PowerSeries/More_on_PowerSeries/Hg.var" "More_on_PowerSeries__".
(* end show *)
inline "cic:/CoRN/transc/PowerSeries/Derivative_FPowerSeries1'.con".
(* UNEXPORTED
-End More_on_PowerSeries.
+End More_on_PowerSeries
*)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
(*#* **Function definitions through power series
inline "cic:/CoRN/transc/PowerSeries/Logarithm.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Power_Function.
+Section Power_Function
*)
(*#* **Power Function
%\end{convention}%
*)
-inline "cic:/CoRN/transc/RealPowers/J.var".
+inline "cic:/CoRN/transc/RealPowers/Power_Function/J.var" "Power_Function__".
-inline "cic:/CoRN/transc/RealPowers/F.var".
+inline "cic:/CoRN/transc/RealPowers/Power_Function/F.var" "Power_Function__".
-inline "cic:/CoRN/transc/RealPowers/G.var".
+inline "cic:/CoRN/transc/RealPowers/Power_Function/G.var" "Power_Function__".
inline "cic:/CoRN/transc/RealPowers/FPower.con".
inline "cic:/CoRN/transc/RealPowers/Continuous_power.con".
(* UNEXPORTED
-End Power_Function.
+End Power_Function
*)
(* NOTATION
*)
(* UNEXPORTED
-Section More_on_Power_Function.
+Section More_on_Power_Function
*)
(* UNEXPORTED
inline "cic:/CoRN/transc/RealPowers/Diffble_power.con".
(* UNEXPORTED
-End More_on_Power_Function.
+End More_on_Power_Function
*)
(* UNEXPORTED
include "transc/Trigonometric.ma".
(* UNEXPORTED
-Section Sum_and_so_on.
+Section Sum_and_so_on
*)
(* UNEXPORTED
(* begin hide *)
-inline "cic:/CoRN/transc/SinCos/F.con".
+inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F.con" "Sum_and_so_on__".
-inline "cic:/CoRN/transc/SinCos/G.con".
+inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G.con" "Sum_and_so_on__".
-inline "cic:/CoRN/transc/SinCos/F'.con".
+inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/F'.con" "Sum_and_so_on__".
-inline "cic:/CoRN/transc/SinCos/G'.con".
+inline "cic:/CoRN/transc/SinCos/Sum_and_so_on/G'.con" "Sum_and_so_on__".
(* end hide *)
inline "cic:/CoRN/transc/SinCos/FFT'.con".
(* UNEXPORTED
-End Sum_and_so_on.
+End Sum_and_so_on
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Basic_Properties.
+Section Basic_Properties
*)
(*#* **Basic properties
inline "cic:/CoRN/transc/SinCos/AbsIR_Sin_less_One.con".
(* UNEXPORTED
-End Basic_Properties.
+End Basic_Properties
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Definitions.
+Section Definitions
*)
-inline "cic:/CoRN/transc/TaylorSeries/J.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/J.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/pJ.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/pJ.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/F.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/F.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/diffF.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/diffF.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/a.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/a.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/Ha.var" "Definitions__".
inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series'.con".
%\end{convention}%
*)
-inline "cic:/CoRN/transc/TaylorSeries/f.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/f.var" "Definitions__".
-inline "cic:/CoRN/transc/TaylorSeries/derF.var".
+inline "cic:/CoRN/transc/TaylorSeries/Definitions/derF.var" "Definitions__".
inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series.con".
inline "cic:/CoRN/transc/TaylorSeries/abs_Taylor_Rem_char.con".
(* UNEXPORTED
-End Definitions.
+End Definitions
*)
(* UNEXPORTED
-Section Convergence_in_IR.
+Section Convergence_in_IR
*)
(*#* **Convergence
[F].
*)
-inline "cic:/CoRN/transc/TaylorSeries/H.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H.var" "Convergence_in_IR__".
-inline "cic:/CoRN/transc/TaylorSeries/F.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/F.var" "Convergence_in_IR__".
-inline "cic:/CoRN/transc/TaylorSeries/a.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/a.var" "Convergence_in_IR__".
-inline "cic:/CoRN/transc/TaylorSeries/Ha.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Ha.var" "Convergence_in_IR__".
-inline "cic:/CoRN/transc/TaylorSeries/f.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/f.var" "Convergence_in_IR__".
-inline "cic:/CoRN/transc/TaylorSeries/derF.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/derF.var" "Convergence_in_IR__".
inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_imp_cont.con".
(* begin show *)
-inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/bndf.var" "Convergence_in_IR__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/transc/TaylorSeries/H1.con".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/H1.con" "Convergence_in_IR__".
(* UNEXPORTED
Transparent nexp_op.
(* begin show *)
-inline "cic:/CoRN/transc/TaylorSeries/Hf.var".
+inline "cic:/CoRN/transc/TaylorSeries/Convergence_in_IR/Hf.var" "Convergence_in_IR__".
(* end show *)
inline "cic:/CoRN/transc/TaylorSeries/Taylor_Series_conv_to_fun.con".
(* UNEXPORTED
-End Convergence_in_IR.
+End Convergence_in_IR
*)
(* UNEXPORTED
-Section Other_Results.
+Section Other_Results
*)
(*#*
Taylor series converge to themselves.
*)
-inline "cic:/CoRN/transc/TaylorSeries/F.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/F.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/G.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/G.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/a.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/a.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/f.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/f.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/g.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/g.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/derF.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/derF.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/derG.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/derG.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/bndf.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/bndf.var" "Other_Results__".
-inline "cic:/CoRN/transc/TaylorSeries/bndg.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/bndg.var" "Other_Results__".
(* begin show *)
-inline "cic:/CoRN/transc/TaylorSeries/Heq.var".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/Heq.var" "Other_Results__".
(* end show *)
(* begin hide *)
-inline "cic:/CoRN/transc/TaylorSeries/Hf.con".
+inline "cic:/CoRN/transc/TaylorSeries/Other_Results/Hf.con" "Other_Results__".
(* end hide *)
inline "cic:/CoRN/transc/TaylorSeries/Taylor_unique_crit.con".
(* UNEXPORTED
-End Other_Results.
+End Other_Results
*)
inline "cic:/CoRN/transc/TrigMon/Sin_resp_less.con".
(* UNEXPORTED
-Section Tangent.
+Section Tangent
*)
(*#* **Derivative of Tangent
inline "cic:/CoRN/transc/TrigMon/Tan_resp_leEq.con".
(* UNEXPORTED
-End Tangent.
+End Tangent
*)
(* UNEXPORTED
*)
(* UNEXPORTED
-Section Lemmas.
+Section Lemmas
*)
(*#* First, we need a lemma on mappings. *)
inline "cic:/CoRN/transc/Trigonometric/maps_translation.con".
(* UNEXPORTED
-End Lemmas.
+End Lemmas
*)
(* UNEXPORTED
-Section Sine_and_Cosine.
+Section Sine_and_Cosine
*)
(*#* Sine, cosine and tangent at [Zero]. *)
*)
(* UNEXPORTED
-Section Sine_of_Sum.
+Section Sine_of_Sum
*)
(*#*
(* begin hide *)
-inline "cic:/CoRN/transc/Trigonometric/F.con".
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline "cic:/CoRN/transc/Trigonometric/G.con".
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline "cic:/CoRN/transc/Trigonometric/F'.con".
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/F'.con" "Sine_and_Cosine__Sine_of_Sum__".
-inline "cic:/CoRN/transc/Trigonometric/G'.con".
+inline "cic:/CoRN/transc/Trigonometric/Sine_and_Cosine/Sine_of_Sum/G'.con" "Sine_and_Cosine__Sine_of_Sum__".
(* end hide *)
inline "cic:/CoRN/transc/Trigonometric/Sin_plus_fun.con".
(* UNEXPORTED
-End Sine_of_Sum.
+End Sine_of_Sum
*)
(* UNEXPORTED
inline "cic:/CoRN/transc/Trigonometric/Cos_plus_fun.con".
(* UNEXPORTED
-End Sine_and_Cosine.
+End Sine_and_Cosine
*)
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/logic/coimplication".
+
+include "logic/connectives.ma".
+
+definition Iff : Prop \to Prop \to Prop \def
+ \lambda A,B. (A \to B) \land (B \to A).
+
+ (*CSC: the URI must disappear: there is a bug now *)
+interpretation "logical iff" 'iff x y = (cic:/matita/logic/coimplication/Iff.con x y).
+
+notation > "hvbox(a break \liff b)"
+ left associative with precedence 25
+for @{ 'iff $a $b }.
+
+notation < "hvbox(a break \leftrightarrow b)"
+ left associative with precedence 25
+for @{ 'iff $a $b }.
+
+theorem iff_intro: \forall A,B. (A \to B) \to (B \to A) \to (A \liff B).
+ unfold Iff. intros. split; intros; auto.
+qed.
+
+theorem iff_refl: \forall A. A \liff A.
+ intros. apply iff_intro; intros; auto.
+qed.
+
+theorem iff_sym: \forall A,B. A \liff B \to B \liff A.
+ intros. decompose. apply iff_intro; intros; auto.
+qed.
+
+theorem iff_trans: \forall A,B,C. A \liff B \to B \liff C \to A \liff C.
+ intros. decompose. apply iff_intro; intros; auto.
+qed.
let t_and_ty = Cic.Cast (term,ty) in
guistuff.mathviewer#show_entry (`Cic (t_and_ty,metasenv));
[], "", parsed_text_length
- | TA.Inline (_,suri) ->
+ | TA.Inline (_,suri,prefix) ->
let dbd = LibraryDb.instance () in
let uris =
let sql_pat =
projects / helm.git / commitdiff