set "baseuri" "cic:/matita/CoRN-Decl/algebra/CAbGroups".
-(* INCLUDE
-CGroups
-*)
+include "CoRN.ma".
+
+include "algebra/CGroups.ma".
(* UNEXPORTED
-Section Abelian_Groups.
+Section Abelian_Groups
*)
(*#*
Now we introduce commutativity and add some results.
*)
-inline cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con.
+inline "cic:/CoRN/algebra/CAbGroups/is_CAbGroup.con".
+
+inline "cic:/CoRN/algebra/CAbGroups/CAbGroup.ind".
-inline cic:/CoRN/algebra/CAbGroups/CAbGroup.ind.
+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.
+alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/AbGroup_Axioms/G.var".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con.
+inline "cic:/CoRN/algebra/CAbGroups/CAbGroup_is_CAbGroup.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_commutes.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_commutes.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_commutes_unfolded.con.
+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.
+alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/G.var".
-inline cic:/CoRN/algebra/CAbGroups/P.var.
+alias id "P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/P.var".
-inline cic:/CoRN/algebra/CAbGroups/Punit.var.
+alias id "Punit" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/Punit.var".
-inline cic:/CoRN/algebra/CAbGroups/op_pres_P.var.
+alias id "op_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/op_pres_P.var".
-inline cic:/CoRN/algebra/CAbGroups/inv_pres_P.var.
+alias id "inv_pres_P" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/SubCAbGroups/inv_pres_P.var".
(*#*
%\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/isabgrp_scrr.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_SubCAbGroup.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.
+alias id "G" = "cic:/CoRN/algebra/CAbGroups/Abelian_Groups/Various/G.var".
(*#*
%\begin{convention}% Let [G] be an Abelian Group.
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbGroups/cag_op_inv.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_op_inv.con".
(* UNEXPORTED
Hint Resolve cag_op_inv: algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/assoc_1.con.
+inline "cic:/CoRN/algebra/CAbGroups/assoc_1.con".
-inline cic:/CoRN/algebra/CAbGroups/minus_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/minus_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con.
+inline "cic:/CoRN/algebra/CAbGroups/op_lft_resp_ap.con".
-inline cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con.
+inline "cic:/CoRN/algebra/CAbGroups/cag_ap_cancel_lft.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_cancel_ap_lft.con.
+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.
+alias id "S" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/S.var".
-inline cic:/CoRN/algebra/CAbGroups/unit.var.
+alias id "unit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/unit.var".
-inline cic:/CoRN/algebra/CAbGroups/plus.var.
+alias id "plus" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus.var".
(*#*
%\begin{convention}%
%\end{convention}%
*)
-inline cic:/CoRN/algebra/CAbGroups/plus_lext.var.
+alias id "plus_lext" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lext.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_lunit.var.
+alias id "plus_lunit" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_lunit.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_comm.var.
+alias id "plus_comm" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_comm.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_assoc.var.
+alias id "plus_assoc" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/plus_assoc.var".
-inline cic:/CoRN/algebra/CAbGroups/inv.var.
+alias id "inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv.var".
-inline cic:/CoRN/algebra/CAbGroups/inv_inv.var.
+alias id "inv_inv" = "cic:/CoRN/algebra/CAbGroups/Nice_Char/inv_inv.var".
-inline cic:/CoRN/algebra/CAbGroups/plus_rext.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_rext.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_runit.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_runit.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_is_fun.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_is_fun.con".
-inline cic:/CoRN/algebra/CAbGroups/inv_inv'.con.
+inline "cic:/CoRN/algebra/CAbGroups/inv_inv'.con".
-inline cic:/CoRN/algebra/CAbGroups/plus_fun.con.
+inline "cic:/CoRN/algebra/CAbGroups/plus_fun.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CSemiGroup'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CMonoid'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con.
+inline "cic:/CoRN/algebra/CAbGroups/Build_CGroup'.con".
-inline cic:/CoRN/algebra/CAbGroups/Build_CAbGroup'.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.
+alias id "G" = "cic:/CoRN/algebra/CAbGroups/Group_Extras/G.var".
-inline cic:/CoRN/algebra/CAbGroups/nmult.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_wd.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_wd.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_one.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_Zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_Zero.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_mult.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_mult.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_inv.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_inv.con".
-inline cic:/CoRN/algebra/CAbGroups/nmult_plus'.con.
+inline "cic:/CoRN/algebra/CAbGroups/nmult_plus'.con".
(* UNEXPORTED
Hint Resolve nmult_wd nmult_Zero nmult_inv nmult_plus nmult_plus': algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/zmult.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult.con".
(*
Lemma Zeq_imp_nat_eq : forall m n:nat, m = n -> m = n.
Qed.
*)
-inline cic:/CoRN/algebra/CAbGroups/zmult_char.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_char.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_wd.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_wd.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_one.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_min_one.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_min_one.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_zero.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_Zero.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_Zero.con".
(* UNEXPORTED
Hint Resolve zmult_zero: algebra.
*)
-inline cic:/CoRN/algebra/CAbGroups/zmult_plus.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_plus.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_mult.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_mult.con".
-inline cic:/CoRN/algebra/CAbGroups/zmult_plus'.con.
+inline "cic:/CoRN/algebra/CAbGroups/zmult_plus'.con".
(* UNEXPORTED
-End Group_Extras.
+End Group_Extras
*)
(* UNEXPORTED