set "baseuri" "cic:/matita/CoRN-Decl/algebra/Cauchy_COF".
+include "CoRN.ma".
+
(* $Id: Cauchy_COF.v,v 1.8 2004/04/23 10:00:54 lcf Exp $ *)
-(* INCLUDE
-COrdCauchy
-*)
+include "algebra/COrdCauchy.ma".
-(* INCLUDE
-RingReflection
-*)
+include "tactics/RingReflection.ma".
(*#*
* The Field of Cauchy Sequences
*)
(* UNEXPORTED
-Section Structure.
+Section Structure
*)
-inline cic:/CoRN/algebra/Cauchy_COF/F.var.
+alias id "F" = "cic:/CoRN/algebra/Cauchy_COF/Structure/F.var".
(*#*
** Setoid Structure
than the other, equality is the negation of the apartness.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_Set.con.
+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_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_eq.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_eq.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_cotrans.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_cotrans.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_symmetric.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_irreflexive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_irreflexive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_eq_tight.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CSetoid.con".
(* UNEXPORTED
-End CSetoid_Structure.
+End CSetoid_Structure
*)
(* UNEXPORTED
-Section Group_Structure.
+Section Group_Structure
*)
(*#*
are specifically proved are just the necessary ones to get the group axioms.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_zero.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_zero.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_lft_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_assoc.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_zero_lft_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_comm.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv_is_inv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_inv_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rinv.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rinv.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CAbGroup.con.
+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
Same comments as previously.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_ap_zero.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_plus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_dist_minus.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_rht_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_comm.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_ap_zero'.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_lft_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_rht_ext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rmult.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rmult.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_assoc.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_one_lft_unit.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CRing.con.
+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
quite straightforwardly.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_integral_domain.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_recip_inverse'.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_CField.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_CField.con".
(* UNEXPORTED
-End Field_Structure.
+End Field_Structure
*)
(* UNEXPORTED
-Section Order.
+Section Order
*)
(*#* ** Order Structure
defined at the beginning.
*)
-inline cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_lt_strext.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_transitive.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_strict.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_plus_resp_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_mult_resp_lt.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_COrdField.con.
+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/Rlt_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Rlt_alt_2.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/R_ap_alt_2.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_1.con".
-inline cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con.
+inline "cic:/CoRN/algebra/Cauchy_COF/Eq_alt_2_2.con".
(* UNEXPORTED
-End Auxiliary.
+End Auxiliary
*)
(* UNEXPORTED
-End Structure.
+End Structure
*)