set "baseuri" "cic:/matita/CoRN-Decl/model/setoids/Qpossetoid".
+include "CoRN.ma".
+
(* $Id: Qpossetoid.v,v 1.4 2004/04/06 15:46:05 lcf Exp $ *)
-(* INCLUDE
-Qsetoid
-*)
+include "model/setoids/Qsetoid.ma".
-(* INCLUDE
-CSetoidFun
-*)
+include "algebra/CSetoidFun.ma".
-(* INCLUDE
-Qpossec
-*)
+include "model/structures/Qpossec.ma".
(*#* **Example of a setoid: [Qpos]
***Setoid
rational numbers.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QposP.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QposP.con".
(*#* One, two and four are elements of it.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QONEpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QTWOpos.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/QFOURpos.con".
(*#* ***Multiplication
As we have seen, multiplication preserves positivity, so we can restrict it
nice properties.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qmult_pres_pos1.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_mult.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/associative_Qpos_mult.con".
(*#* ***Inverse
We restrict the domain of the inverse to the set of positive rationals.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_inv.con".
(*#* The restricted inverse preserves positivity.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/inv_pres_pos1.con".
(*#* Now, we can also restrict the co-domain.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv.con".
(*#* This restricted inverse map appears a setoid function.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_strong_ext.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_Qpos_inv_op.con".
(*#* ***Special multiplication and inverse
We define [multdiv2]: $(x,y) \mapsto xy/2$ #(x,y) ↦ xy/2#.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/Qpos_div2.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/multdiv2.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/associative_multdiv2.con".
(*#* And its inverse [multdiv4]: $x \mapsto 4/x$ #x ↦ 4/x#.
*)
-inline cic:/CoRN/model/setoids/Qpossetoid/mult4.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/mult4.con".
-inline cic:/CoRN/model/setoids/Qpossetoid/divmult4.con.
+inline "cic:/CoRN/model/setoids/Qpossetoid/divmult4.con".