set "baseuri" "cic:/matita/CoRN-Decl/model/structures/Zsec".
+include "CoRN.ma".
+
(* $Id: Zsec.v,v 1.5 2004/04/06 15:46:05 lcf Exp $ *)
(*#* printing {#Z} %\ensuremath{\mathrel\#_{\mathbb Z}}% *)
-(* INCLUDE
-ZArith
-*)
-
-(* INCLUDE
-CLogic
-*)
+include "algebra/CLogic.ma".
(*#* *[Z]
** About [Z]
We define the apartness as the negation of the Leibniz equality:
*)
-inline cic:/CoRN/model/structures/Zsec/ap_Z.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z.con".
+
+(* NOTATION
+Infix "{#Z}" := ap_Z (no associativity, at level 90).
+*)
(*#* Some properties of apartness:
*)
-inline cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_irreflexive0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_symmetric0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_cotransitive0.con".
-inline cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con.
+inline "cic:/CoRN/model/structures/Zsec/ap_Z_tight0.con".
-inline cic:/CoRN/model/structures/Zsec/ONE_neq_O.con.
+inline "cic:/CoRN/model/structures/Zsec/ONE_neq_O.con".
(*#* ***Addition
Some properties of the addition. [Zplus] is also defined in the standard
library.
*)
-inline cic:/CoRN/model/structures/Zsec/Zplus_wd0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zplus_wd0.con".
-inline cic:/CoRN/model/structures/Zsec/Zplus_strext0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zplus_strext0.con".
(*#* ***Multiplication
The multiplication is extensional:
*)
-inline cic:/CoRN/model/structures/Zsec/Zmult_strext0.con.
+inline "cic:/CoRN/model/structures/Zsec/Zmult_strext0.con".
(*#* ***Miscellaneous
*)
-inline cic:/CoRN/model/structures/Zsec/Zpos.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos.con".
(* begin hide *)
+coercion cic:/Coq/ZArith/BinInt/Z.ind#xpointer(1/1/2) 0 (* compounds *).
+
(* end hide *)
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma1.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma2.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma3.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma4.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_pos.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_pos.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_neg.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_neg.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn.con".
-inline cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con.
+inline "cic:/CoRN/model/structures/Zsec/Zpos_Zsgn2.con".
-inline cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con.
+inline "cic:/CoRN/model/structures/Zsec/a_very_specific_lemma5'.con".