elim implemented as a notation for apply

diff --git a/matita/matita/tests/nelim-userspace.ma b/matita/matita/tests/nelim-userspace.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 "hints_declaration.ma".
+
+nrecord eliminator (P_ : Prop) (T_ : Type[1]) : Type[1] ≝ {
+  indty : Type[0];
+  elimP : indty → P_;
+  elimT : indty → T_
+}.
+
+notation "\elim term 90 x term 90 P" non associative with precedence 90 
+for @{'elim ?? ? $x … $P … $x}.
+interpretation "elimP" 'elim = elimP.
+interpretation "elimT" 'elim = elimT.
+
+ninductive nat : Type[0] ≝ O : nat | S : nat → nat.
+
+ndefinition eP ≝ mk_eliminator ?? nat (λ_.nat_ind) (λ_.nat_rect_Type0).
+
+alias symbol "hint_decl" (instance 1) = "hint_decl_Type1".
+unification hint 0 ≔;
+  X ≟ eP
+(*-----------------------------------------*) ⊢
+  indty ?? X ≡ nat.
+  
+ninductive list (A : Type[0]) : nat → Type[0] ≝ 
+| nil : list A O
+| cons : ∀n.A → list A n → list A (S n).
+
+ndefinition eL ≝ λA,n.
+  mk_eliminator ?? (list A n) (λ_.list_ind A) (λ_.list_rect_Type0 A).
+
+alias symbol "hint_decl" (instance 1) = "hint_decl_Type1".
+unification hint 0 ≔ A,n;
+  X ≟ eL A n
+(*-----------------------------------------*) ⊢
+  indty ?? X ≡ list A n.  
+
+naxiom A : ∀n1,n2.∀l1:list nat n1.∀l2:list nat n2.Prop.
+
+nlemma xxx : ∀n.∀x:list nat n.A ?? x x.
+#n; #l;
+napply (\elim l (λd,y.A ?? y l)); 
+
+
+##[ ##| #len e l1 Pl1;
+napply ((\elim ?? ? x) … x); #;#[ napply eP]
+
+
+nrecord eliminator (indty : Type[0]) 
+                   (s : Type[2])    
+                   (t : Type[1]) : Type[2] ≝ {
+  elimp : t
+}.
+
+
+ndefinition P :
+  ?
+≝  
+  λity,s,t.λR : eliminator ity s t. λG:s.
+   match R with [ mk_eliminator _ ⇒ G].
+
+ninductive nat : Type[0] ≝ O : nat | S : nat → nat.
+
+ndefinition eP := mk_eliminator nat Prop    ? nat_ind.
+ndefinition eT := mk_eliminator nat Type[0] ? nat_rect_Type0.
+
+unification hint 0 ≔ G;
+  X ≟ eP
+(*-----------------------------------------*) ⊢
+  P nat Prop ? X G ≡ G.
+  (*
+unification hint 0 ≔ G;
+  X ≟ eT
+(*-----------------------------------------*) ⊢
+  P nat Type[0] ? X G ≡ G.
+  *)
+
+nlemma A : nat.
+napply (
+
+ndefinition elim_gen : 
+  ∀ity:Type[0].∀s,t.∀x:ity.
+    ∀e:eliminator ity s t.∀G.P ity s t e G 
+≝
+  λity,s,t,x,e,G.elimp ??? e x.