X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FdiscriminationTactics.ml;fp=helm%2Focaml%2Ftactics%2FdiscriminationTactics.ml;h=9e5bc7f43e1d3885225d6f3ecd24dbab01faab73;hp=0000000000000000000000000000000000000000;hb=792b5d29ebae8f917043d9dd226692919b5d6ca1;hpb=a14a8c7637fd0b95e9d4deccb20c6abc98e8f953

diff --git a/helm/ocaml/tactics/discriminationTactics.ml b/helm/ocaml/tactics/discriminationTactics.ml
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+(* Copyright (C) 2002, HELM Team.
+ * 
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ * 
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ * 
+ * HELM 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 for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA  02111-1307, USA.
+ * 
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* $Id$ *)
+
+let debug_print = fun _ -> ()
+
+let rec injection_tac ~term =
+ let injection_tac ~term status = 
+  let (proof, goal) = status in
+  let module C = Cic in
+  let module U = UriManager in
+  let module P = PrimitiveTactics in
+  let module T = Tacticals in
+  let _,metasenv,_,_ = proof in
+  let _,context,_ = CicUtil.lookup_meta goal metasenv in
+  let termty,_ = (* TASSI: FIXME *)
+    CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in  
+    ProofEngineTypes.apply_tactic
+      (match termty with
+          (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+             when LibraryObjects.is_eq_URI equri -> (
+           match tty with
+              (C.MutInd (turi,typeno,exp_named_subst))
+            | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> (
+                   match t1,t2 with
+                      ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                         when (uri1 = uri2) && (typeno1 = typeno2) && 
+			      (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
+                       (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
+                         when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
+                       let rec traverse_list i l1 l2 =
+                         match l1,l2 with
+                            [],[] -> T.id_tac
+                          | hd1::tl1,hd2::tl2 -> 
+                             T.then_ 
+                              ~start:(injection1_tac ~i ~term)
+                              ~continuation:(traverse_list (i+1) tl1 tl2)
+                          | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???"))
+                       in traverse_list 1 applist1 applist2
+                    | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                    | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
+                         when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
+                       (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac
+                    | _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac
+                   )
+            | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
+           )
+        | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
+      ) status
+ in 
+  ProofEngineTypes.mk_tactic (injection_tac ~term)
+
+and injection1_tac ~term ~i = 
+ let injection1_tac ~term ~i status =
+  let (proof, goal) = status in
+  (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
+   let module C = Cic in
+   let module S = CicSubstitution in
+   let module U = UriManager in
+   let module P = PrimitiveTactics in
+   let module T = Tacticals in
+   let _,metasenv,_,_ = proof in
+   let _,context,_ = CicUtil.lookup_meta goal metasenv in
+   let termty,_ = (* TASSI: FIXME *)
+     CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+     match termty with (* an equality *)
+         (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+             when LibraryObjects.is_eq_URI equri -> (
+           match tty with (* some inductive type *)
+              (C.MutInd (turi,typeno,exp_named_subst))
+            | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
+               let t1',t2',consno = (* sono i due sottotermini che differiscono *)
+                match t1,t2 with
+                   ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
+                    (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
+                      when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
+                    (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
+                 | _ -> assert false
+               in
+                let tty',_ = 
+		  CicTypeChecker.type_of_aux' metasenv context t1' 
+		    CicUniv.empty_ugraph  in
+                let pattern =
+                      match fst(CicEnvironment.get_obj 
+				  CicUniv.empty_ugraph turi ) with
+                         C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx,_)  ->
+                          let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
+                           let i_constr_id,_ = List.nth constructor_list (consno - 1) in
+                            List.map
+                             (function (id,cty) ->
+                               let reduced_cty = CicReduction.whd context cty in
+                                let rec aux t k =
+                                 match t with
+                                    C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
+                                     aux target (k+1)
+                                  | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
+ 				    let binder' =
+                                      match binder with
+                                         C.Name b -> C.Name b
+                                       | C.Anonymous -> C.Name "y"
+                                     in
+                                      C.Lambda (binder',source,(aux target (k+1)))
+                                  | _ ->
+                                     let nr_param_constr = k - 1 - nr_ind_params_dx in
+                                      if (id = i_constr_id)
+                                       then C.Rel (nr_param_constr - i + 1)
+                                       else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
+                                in aux reduced_cty 1
+                             )
+                             constructor_list
+                       | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible"))
+                in
+                ProofEngineTypes.apply_tactic   
+                 (T.thens 
+                  ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
+                  ~continuations:[
+                    T.then_ 
+                     ~start:(injection_tac ~term:(C.Rel 1))
+                     ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *) 
+                    ;
+                    T.then_ 
+                     ~start:(ProofEngineTypes.mk_tactic 
+                       (fun status ->    
+                         let (proof, goal) = status in
+                         let _,metasenv,_,_ = proof in
+                          let _,context,gty = CicUtil.lookup_meta goal metasenv in
+                           let new_t1' = 
+                            match gty with 
+                               (C.Appl (C.MutInd (_,_,_)::arglist)) -> 
+                                List.nth arglist 1
+                             | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: goal after cut is not correct"))
+                           in
+                            ProofEngineTypes.apply_tactic 
+                            (ReductionTactics.change_tac
+                               ~pattern:(ProofEngineTypes.conclusion_pattern
+                                (Some new_t1'))
+                               (fun _ m u ->
+                                 C.Appl [ C.Lambda (C.Name "x", tty,
+                                  C.MutCase (turi, typeno,
+                                   (C.Lambda ((C.Name "x"),
+                                    (S.lift 1 tty),
+                                    (S.lift 2 tty'))),
+                                   (C.Rel 1), pattern
+                                  )
+                                 );
+                                 t1], m, u))
+                        status
+                       ))
+                     ~continuation:
+                       (T.then_
+                         ~start:
+                           (EqualityTactics.rewrite_simpl_tac
+                             ~direction:`LeftToRight
+                             ~pattern:(ProofEngineTypes.conclusion_pattern None)
+                             term)
+                         ~continuation:EqualityTactics.reflexivity_tac
+                       )
+                   ])     
+                  status
+            | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not a discriminable equality"))
+           )
+        | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not an equality"))
+ in
+  ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
+;;
+
+exception TwoDifferentSubtermsFound of int 
+
+(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
+diversi *)
+
+let discriminate'_tac ~term =
+ let module C = Cic in
+ let module U = UriManager in
+ let module P = PrimitiveTactics in
+ let module T = Tacticals in
+ let fail msg = raise (ProofEngineTypes.Fail (lazy ("Discriminate: " ^ msg))) in
+ let find_discriminating_consno t1 t2 =
+   let rec aux t1 t2 =
+     match t1, t2 with
+     | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
+     | C.Appl ((C.MutConstruct _ as constr1) :: args1),
+       C.Appl ((C.MutConstruct _ as constr2) :: args2)
+       when constr1 = constr2 ->
+         let rec aux_list l1 l2 =
+           match l1, l2 with
+           | [], [] -> None
+           | hd1 :: tl1, hd2 :: tl2 ->
+               (match aux hd1 hd2 with
+               | None -> aux_list tl1 tl2
+               | Some _ as res -> res)
+           | _ -> (* same constructor applied to a different number of args *)
+               assert false
+         in
+         aux_list args1 args2
+     | ((C.MutConstruct (_,_,consno1,subst1)),
+       (C.MutConstruct (_,_,consno2,subst2)))
+     | ((C.MutConstruct (_,_,consno1,subst1)),
+       (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+     | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+       (C.MutConstruct (_,_,consno2,subst2)))
+     | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
+       (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
+       when (consno1 <> consno2) || (subst1 <> subst2) ->
+         Some consno2
+     | _ -> fail "not a discriminable equality"
+   in
+   aux t1 t2
+ in
+ let mk_pattern turi typeno consno context left_args =
+    (* a list of "True" except for the element in position consno which
+     * is "False" *)
+    match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
+    | C.InductiveDefinition (ind_type_list,_,nr_ind_params,_)  ->
+        let _,_,_,constructor_list = List.nth ind_type_list typeno in 
+        let false_constr_id,_ = List.nth constructor_list (consno - 1) in
+        List.map 
+          (fun (id,cty) ->
+            (* dubbio: e' corretto ridurre in questo context ??? *)
+            let red_ty = CicReduction.whd context cty in
+            let rec aux t k =
+              match t with
+              | C.Prod (_,_,target) when (k <= nr_ind_params) ->
+                  CicSubstitution.subst (List.nth left_args (k-1))
+                    (aux target (k+1))
+              | C.Prod (binder,source,target) when (k > nr_ind_params) ->
+                  C.Lambda (binder, source, (aux target (k+1)))
+              | _ -> 
+                  if (id = false_constr_id)
+                  then (C.MutInd(LibraryObjects.false_URI (),0,[]))
+                  else (C.MutInd(LibraryObjects.true_URI (),0,[]))
+            in
+            (CicSubstitution.lift 1 (aux red_ty 1)))
+          constructor_list
+    | _ -> (* object is not an inductive definition *)
+        assert false
+ in
+ let discriminate'_tac ~term status = 
+  let (proof, goal) = status in
+  let _,metasenv,_,_ = proof in
+  let _,context,_ = CicUtil.lookup_meta goal metasenv in
+  let termty,_ = 
+    CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
+  in
+  match termty with
+  | (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+    when LibraryObjects.is_eq_URI equri ->
+      let turi,typeno,exp_named_subst,left_args = 
+        match tty with
+        | (C.MutInd (turi,typeno,exp_named_subst)) ->
+            turi,typeno,exp_named_subst,[]
+        | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::left_args)) ->
+            turi,typeno,exp_named_subst,left_args
+        | _ -> fail "not a discriminable equality"
+      in
+      let consno =
+        match find_discriminating_consno t1 t2 with
+        | Some consno -> consno
+        | None -> fail "discriminating terms are structurally equal"
+      in
+      let pattern = mk_pattern turi typeno consno context left_args in
+      let (proof',goals') = 
+        ProofEngineTypes.apply_tactic 
+          (EliminationTactics.elim_type_tac
+            (C.MutInd (LibraryObjects.false_URI (), 0, [])))
+          status 
+      in
+      (match goals' with
+      | [goal'] -> 
+          let _,metasenv',_,_ = proof' in
+          let _,context',gty' = CicUtil.lookup_meta goal' metasenv' in
+          ProofEngineTypes.apply_tactic
+            (T.then_
+              ~start:
+                (ReductionTactics.change_tac 
+                  ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty'))
+                  (fun _ m u ->
+                    C.Appl [
+                      C.Lambda ( C.Name "x", tty,
+                        C.MutCase (turi, typeno,
+                          (C.Lambda ((C.Name "x"),
+                           (CicSubstitution.lift 1 tty),
+                           (C.Sort C.Prop))),
+                          (C.Rel 1), pattern));
+                      t2 ], m, u))
+              ~continuation:
+                (T.then_
+                  ~start:
+                    (EqualityTactics.rewrite_simpl_tac
+                      ~direction:`RightToLeft
+                      ~pattern:(ProofEngineTypes.conclusion_pattern None)
+                      term)
+                  ~continuation:
+                    (IntroductionTactics.constructor_tac ~n:1)))
+            (proof',goal')
+      | [] -> fail "ElimType False left no goals"
+      | _ -> fail "ElimType False left more than one goal")
+    | _ -> fail "not an equality"
+  in
+  ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
+
+let discriminate_tac ~term = 
+ let discriminate_tac ~term status =
+  ProofEngineTypes.apply_tactic 
+  (Tacticals.then_
+    ~start:(* (injection_tac ~term) *) Tacticals.id_tac
+    ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
+   status
+ in
+  ProofEngineTypes.mk_tactic (discriminate_tac ~term)
+
+let decide_equality_tac =
+(* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
+e' vera o no e lo risolve *)
+  Tacticals.id_tac
+
+let compare_tac ~term = Tacticals.id_tac
+ (*
+(* term is in the form t1=t2; the tactic leaves two goals: in the first you have to          *)
+(* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2  *)
+  let module C = Cic in
+  let module U = UriManager in
+  let module P = PrimitiveTactics in
+  let module T = Tacticals in
+   let _,metasenv,_,_ = proof in
+    let _,context,gty = CicUtil.lookup_meta goal metasenv in
+     let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
+      match termty with
+         (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
+          
+          let term' = (* (t1=t2)\/~(t1=t2) *)
+           C.Appl [
+            (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ; 
+            term ; 
+            C.Appl [
+             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ; 
+             t1 ; 
+             C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
+            ]
+           ] 
+          in
+            T.thens 
+               ~start:(P.cut_tac ~term:term')
+               ~continuations:[
+                 T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ; 
+                 decide_equality_tac]  
+               status
+      | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
+          let term' = (* (t1=t2) \/ ~(t1=t2) *)
+           C.Appl [
+            (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ; 
+            term ; 
+            C.Appl [
+             (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ; 
+             t1 ; 
+             C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
+            ]
+           ] 
+          in
+            T.thens 
+               ~start:(P.cut_tac ~term:term')
+               ~continuations:[
+                 T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ; 
+                 decide_equality_tac]  
+               status
+      | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality") 
+*)
+;;
+
+
+
+(* DISCRIMINTATE SENZA INJECTION 
+
+exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int) 
+
+let discriminate_tac ~term status =
+  let module C = Cic in
+  let module U = UriManager in
+  let module P = PrimitiveTactics in
+  let module T = Tacticals in
+  let (proof, goal) = status in
+   let _,metasenv,_,_ = proof in
+    let _,context,_ = CicUtil.lookup_meta goal metasenv in
+     let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
+      match termty with
+         (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) 
+          when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) 
+            or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
+           match tty with
+              (C.MutInd (turi,typeno,exp_named_subst))
+            | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
+
+                let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
+                 try
+                  let rec traverse t1 t2 =
+debug_print (lazy ("XXXX t1 " ^ CicPp.ppterm t1)) ;
+debug_print (lazy ("XXXX t2 " ^ CicPp.ppterm t2)) ;
+                   match t1,t2 with
+                      ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                         when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
+                       t1,t2,0
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2))) 
+                         when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
+                       let rec traverse_list l1 l2 =
+                         match l1,l2 with
+                            [],[] -> t1,t2,0
+                          | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
+                          | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
+                       in traverse_list applist1 applist2
+
+                    | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                    | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
+                       (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
+                    | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
+                       (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
+                         when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
+                       raise (TwoDifferentSubtermsFound (t1,t2,consno2))
+                    | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
+                  in traverse t1 t2
+                 with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
+                in
+debug_print (lazy ("XXXX consno2' " ^ (string_of_int consno2'))) ;
+                 if consno2' = 0 
+                  then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
+                  else
+
+                   let pattern = 
+                     (* a list of "True" except for the element in position consno2' which is "False" *)
+                     match fst(CicEnvironment.get_obj turi 
+                                 CicUniv.empty_ugraph) with
+                        C.InductiveDefinition (ind_type_list,_,nr_ind_params)  ->
+debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno))) ;
+                         let _,_,_,constructor_list = (List.nth ind_type_list typeno) in 
+debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2'))) ;
+                          let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
+debug_print (lazy "XXXX nth funzionano ") ;
+                           List.map 
+                            (function (id,cty) ->
+                              let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
+                               let rec aux t k =
+                                match t with
+                                   C.Prod (_,_,target) when (k <= nr_ind_params) ->
+                                    aux target (k+1)
+                                 | C.Prod (binder,source,target) when (k > nr_ind_params) -> 
+                                    C.Lambda (binder,source,(aux target (k+1)))
+                                 | _ -> 
+                                    if (id = false_constr_id)
+                                     then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
+                                     else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 [])
+                               in aux red_ty 1
+                            ) 
+                            constructor_list
+                      | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
+                   in
+
+                    let (proof',goals') = 
+                     EliminationTactics.elim_type_tac 
+                      ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] ) 
+                      status 
+                    in
+                     (match goals' with
+                         [goal'] -> 
+                          let _,metasenv',_,_ = proof' in
+                           let _,context',gty' =
+                             CicUtil.lookup_meta goal' metasenv'
+                           in
+                            T.then_
+                             ~start:
+                              (P.change_tac 
+                               ~what:gty' 
+                               ~with_what:
+                                (C.Appl [
+                                  C.Lambda (
+                                   C.Name "x", tty, 
+                                   C.MutCase (
+                                    turi, typeno,
+                                    (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
+                                    (C.Rel 1), pattern
+                                   )
+                                  ); 
+                                  t2']
+                                )
+                              )
+                             ~continuation:
+                              (
+debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))));
+debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))) ;
+debug_print (lazy ("XXXX equri: " ^ U.string_of_uri equri)) ;
+debug_print (lazy ("XXXX tty : " ^ CicPp.ppterm tty)) ;
+debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
+debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
+if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
+if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
+if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2') 
+ then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
+ metasenv' context' t1'))) ; debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
+
+                               let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
+                                let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
+
+debug_print (lazy ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term)));
+                                 T.then_
+                                   ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
+                                   ~continuation:(IntroductionTactics.constructor_tac ~n:1) 
+                              )
+                             (proof',goal')
+                       | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
+                     )    
+            | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
+           )
+       | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
+;;
+
+*)
+
+
+