branch for universe

[helm.git] / matita / tests / dependent_guarded_bove_capretta.ma

diff --git a/matita/tests/dependent_guarded_bove_capretta.ma b/matita/tests/dependent_guarded_bove_capretta.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "nat/nat.ma".
+
+inductive T : Prop :=
+ | l : T
+ | r : T-> T.
+
+inductive Q : nat -> T -> Prop :=
+ | lq : Q O l
+ | lr : ∀n,t.Q (S (S n)) t -> Q n (r t). 
+ 
+axiom F : False. 
+
+definition xxx := λt.(match t return (λt:T.T) with 
+    [ l => match F in False with [] 
+    | r (t1:T) => t1]).
+ 
+let rec f (n:nat) (t:T) on t :nat :=
+  (match n with
+  [ O => O
+  | S mmm =>
+    f (S (S mmm)) (xxx t)]).
+ 
+let rec f (n:nat) (t:T) on t : Q n t -> nat :=
+  (match n with
+  [ O => λ_.O
+  | S mmm => λq:Q (S mmm) (r t). 
+    f (S (S mmm))
+    (match t return (λt:T.T) with 
+    [ l => match F in False with [] 
+    | r (t1:T) => t1])
+    
+    (match q return λn,t,x.Q (S (S n)) t with 
+     [ lq => match F in False return λ_.Q (S (S n)) t with [] 
+     | lr k t qsskt => qsskt])
+    ]). 
+