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diff --git a/matita/tests/pirrel.ma b/matita/tests/pirrel.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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/test/".
-
-include "logic/connectives.ma".
-include "logic/equality.ma".
-
-axiom T : Type.
-
-definition step ≝ λa,b,c:T.λH1:a=b.λH2:a=c. eq_ind T ? (λx.b = x) H1 ? H2.
-
-lemma stepH : ∀a:T.∀H:a=a. step ? ? ? H H = refl_eq T a.
-intros (a H); cases H; reflexivity.
-qed.
-
-axiom decT : ∀a,b:T. a = b ∨ a ≠ b.
-
-lemma nu : ∀a,b:T. ∀E:a=b. a=b.
-intros (a b E); cases (decT a b) (Ecanonical Abs); [ exact H | cases (H E) ]
-qed.
-
-lemma nu_k : ∀a,b:T. ∀E1,E2:a=b. nu ? ? E1 = nu ? ? E2.
-intros (a b E1 E2); unfold nu; 
-cases (decT a b); simplify; [ reflexivity | cases (H E1) ]
-qed.
-
-definition nu_inv ≝ λa,b:T. λE:a=b. step ? ? ? (nu ? ? (refl_eq ? a)) E. 
-
-definition cancel ≝ λA,B:Type.λf.λg:A→B.∀x:A.f (g x) = x.
-
-lemma cancel_nu_nu_inv : ∀a,b:T. cancel (a=b) (a=b) (nu_inv a b) (nu a b).
-intros (a b); unfold cancel; intros (E); cases E;
-unfold nu_inv; rewrite > stepH; reflexivity.
-qed.
-
-lemma pirrel :  ∀a,b:T.∀E1,E2:a=b. E1 = E2.
-intros (a b E1 E2);
-rewrite < cancel_nu_nu_inv; 
-rewrite < cancel_nu_nu_inv in ⊢ (? ? ? %);
-rewrite > (nu_k ? ? E1 E2).
-reflexivity.
-qed.
-
-(* some more tests *)
-inductive eq4 (A : Type) (x : A) (y : A) : A → A → Prop ≝ 
-  eq_refl4 : eq4 A x y x y.
-  
-lemma step4 : ∀a,b:T.∀H:eq4 T a b a b. 
-  eq4_ind T a b (λx,y.eq4 T x y a b) H a b H = eq_refl4 T a b.
-intros (a b H). cases H. reflexivity.
-qed.