--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(* Progetto FreeScale *)
+(* *)
+(* Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it *)
+(* Sviluppo: 2008-2010 *)
+(* *)
+(* ********************************************************************** *)
+
+include "common/theory.ma".
+
+(* coppia dipendente *)
+
+ninductive sigma (A:Type) (P:A → Type) : Type ≝
+ sigma_intro: ∀x:A.P x → sigma A P.
+
+notation < "hvbox(\Sigma ident i opt (: tx) break . p)"
+ right associative with precedence 20
+for @{ 'Sigma ${default
+ @{\lambda ${ident i} : $tx. $p}
+ @{\lambda ${ident i} . $p}}}.
+
+notation > "\Sigma list1 ident x sep , opt (: T). term 19 Px"
+ with precedence 20
+ for ${ default
+ @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}:$T.$acc)} } }
+ @{ ${ fold right @{$Px} rec acc @{'Sigma (λ${ident x}.$acc)} } }
+ }.
+
+notation "\ll term 19 a, break term 19 b \gg"
+with precedence 90 for @{'dependent_pair (λx:?.? x) $a $b}.
+interpretation "dependent pair" 'dependent_pair \eta.c a b = (sigma_intro ? c a b).
+
+interpretation "sigma" 'Sigma \eta.x = (sigma ? x).
+
+ndefinition sigmaFst ≝
+λT:Type.λf:T → Type.λs:sigma T f.match s with [ sigma_intro x _ ⇒ x ].
+ndefinition sigmaSnd ≝
+λT:Type.λf:T → Type.λs:sigma T f.match s return λs.f (sigmaFst ?? s) with [ sigma_intro _ x ⇒ x ].