set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Zsetoid".
+include "CoRN.ma".
+
(* $Id: Zsetoid.v,v 1.5 2004/04/07 15:08:08 lcf Exp $ *)
-(* INCLUDE
-Zsec
-*)
+include "model/structures/Zsec.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
(*#* **Example of a setoid: [Z]
*** [Z]
*)
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_irreflexive.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_symmetric.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_cotransitive.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_tight.con".
-inline cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/ap_Z_is_apartness.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Z_as_CSetoid.con".
(*#* The term [Z_as_CSetoid] is of type [CSetoid]. Hence we have proven that [Z] is a constructive setoid.
***Addition
We will prove now that the addition on the integers is a setoid function.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_bin_fun.con".
(*#* What's more: the addition is also associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_assoc.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zplus_is_commut.con".
(*#* ***Opposite
Taking the opposite of an integer is a setoid function.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zopp_is_fun.con".
(*#* ***Multiplication
Finally the multiplication is a setoid function and is associative and commutative.
*)
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_wd.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_strext.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_bin_fun.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_assoc.con".
-inline cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con.
+inline "cic:/CoRN/model/setoids/Zsetoid/Zmult_is_commut.con".