(*
 * The Why certification tool
 * Copyright (C) 2002 Jean-Christophe FILLIATRE
 * 
 * This software is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public
 * License version 2, as published by the Free Software Foundation.
 * 
 * This software is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 * 
 * See the GNU General Public License version 2 for more details
 * (enclosed in the file GPL).
 *)

(* $Id: WhyTuples.v,v 1.6 2006-11-02 09:18:20 hubert Exp $ *)

(* Tuples *)

Definition tuple_1 (X:Set) := X.

Definition tuple_2 := prod.
Definition Build_tuple_2 (A:Set) (B:Set) := pair A B.
Implicit Arguments Build_tuple_2.
Definition proj_2_1 := fst.
Definition proj_2_2 := snd.

Record tuple_3 (T1 T2 T3:Set) : Set := 
  {proj_3_1 : T1; proj_3_2 : T2; proj_3_3 : T3}.
Implicit Arguments Build_tuple_3.

Record tuple_4 (T1 T2 T3 T4:Set) : Set := 
  {proj_4_1 : T1; proj_4_2 : T2; proj_4_3 : T3; proj_4_4 : T4}.
Implicit Arguments Build_tuple_4.

Record tuple_5 (T1 T2 T3 T4 T5:Set) : Set := 
  {proj_5_1 : T1;
   proj_5_2 : T2;
   proj_5_3 : T3;
   proj_5_4 : T4;
   proj_5_5 : T5}.
Implicit Arguments Build_tuple_5.

Record tuple_6 (T1 T2 T3 T4 T5 T6:Set) : Set := 
  {proj_6_1 : T1;
   proj_6_2 : T2;
   proj_6_3 : T3;
   proj_6_4 : T4;
   proj_6_5 : T5;
   proj_6_6 : T6}.
Implicit Arguments Build_tuple_6.

Record tuple_7 (T1 T2 T3 T4 T5 T6 T7:Set) : Set := 
  {proj_7_1 : T1;
   proj_7_2 : T2;
   proj_7_3 : T3;
   proj_7_4 : T4;
   proj_7_5 : T5;
   proj_7_6 : T6;
   proj_7_7 : T7}.
Implicit Arguments Build_tuple_7.


(* Existentials *)

Definition sig_1 := sig.
Definition exist_1 := exist.
Implicit Arguments exist_1 [A].

Inductive sig_2 (T1 T2:Set) (P:T1 -> T2 -> Prop) : Set :=
    exist_2 : forall (x1:T1) (x2:T2), P x1 x2 -> sig_2 T1 T2 P.
Implicit Arguments exist_2 [T1 T2].

Inductive sig_3 (T1 T2 T3:Set) (P:T1 -> T2 -> T3 -> Prop) : Set :=
    exist_3 :
      forall (x1:T1) (x2:T2) (x3:T3), P x1 x2 x3 -> sig_3 T1 T2 T3 P.
Implicit Arguments exist_3 [T1 T2 T3].

Inductive sig_4 (T1 T2 T3 T4:Set) (P:T1 -> T2 -> T3 -> T4 -> Prop) :
Set :=
    exist_4 :
      forall (x1:T1) (x2:T2) (x3:T3) (x4:T4),
        P x1 x2 x3 x4 -> sig_4 T1 T2 T3 T4 P.
Implicit Arguments exist_4 [T1 T2 T3 T4].

Inductive sig_5 (T1 T2 T3 T4 T5:Set)
(P:T1 -> T2 -> T3 -> T4 -> T5 -> Prop) : Set :=
    exist_5 :
      forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5),
        P x1 x2 x3 x4 x5 -> sig_5 T1 T2 T3 T4 T5 P.
Implicit Arguments exist_5 [T1 T2 T3 T4 T5].

Inductive sig_6 (T1 T2 T3 T4 T5 T6:Set)
(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> Prop) : Set :=
    exist_6 :
      forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) (x6:T6),
        P x1 x2 x3 x4 x5 x6 -> sig_6 T1 T2 T3 T4 T5 T6 P.
Implicit Arguments exist_6 [T1 T2 T3 T4 T5 T6].

Inductive sig_7 (T1 T2 T3 T4 T5 T6 T7:Set)
(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> T7 -> Prop) : Set :=
    exist_7 :
      forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) (x6:T6) (x7:T7),
        P x1 x2 x3 x4 x5 x6 x7 -> sig_7 T1 T2 T3 T4 T5 T6 T7 P.
Implicit Arguments exist_7 [T1 T2 T3 T4 T5 T6 T7].

Inductive sig_8 (T1 T2 T3 T4 T5 T6 T7 T8:Set)
(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> T7 -> T8 -> Prop) : Set :=
    exist_8 :
      forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) (x6:T6) (x7:T7)
        (x8:T8),
        P x1 x2 x3 x4 x5 x6 x7 x8 -> sig_8 T1 T2 T3 T4 T5 T6 T7 T8 P.
      Implicit Arguments exist_8 [T1 T2 T3 T4 T5 T6 T7 T8].

(***
Inductive dep_tuple_2 [ T1,T2 : Set; P:T1->T2->Set ] : Set := 
  Build_dep_tuple_2 : (x1:T1)(x2:T2)(P x1 x2) -> (dep_tuple_2 T1 T2 P).

Inductive dep_tuple_3 [ T1,T2,T3 : Set; P:T1->T2->T3->Set ] : Set := 
  Build_dep_tuple_3 : (x1:T1)(x2:T2)(x3:T3)(P x1 x2 x3)
      	       	   -> (dep_tuple_3 T1 T2 T3 P).
***)


