]> matita.cs.unibo.it Git - helm.git/blobdiff - helm/gTopLevel/fourierR.ml
- bug fixed: some liftings were missing in the implementation of rewrite
[helm.git] / helm / gTopLevel / fourierR.ml
index 446b2ef4b0ac92f95be24194ee6021fc5cb78f27..c46973e2cbeffab6cffc4a95224136ffb4603d07 100644 (file)
  *)
 
 
+(******************** OTHER USEFUL TACTICS **********************)
+
+let rewrite_tac ~term:equality ~status:(proof,goal) =
+ let module C = Cic in
+ let module U = UriManager in
+  let curi,metasenv,pbo,pty = proof in
+  let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
+   let eq_ind_r,ty,t1,t2 = 
+    match CicTypeChecker.type_of_aux' metasenv context equality with
+       C.Appl [C.MutInd (uri,_,0) ; ty ; t1 ; t2]
+        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/Equality/eq.ind") ->
+         let eq_ind_r =
+          C.Const
+           (U.uri_of_string "cic:/Coq/Init/Logic/Logic_lemmas/eq_ind_r.con",0)
+         in
+          eq_ind_r,ty,t1,t2
+     | C.Appl [C.MutInd (uri,_,0) ; ty ; t1 ; t2]
+        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
+         let eqT_ind_r =
+          C.Const
+           (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",0)
+         in
+          eqT_ind_r,ty,t1,t2
+     | _ ->
+       raise
+        (ProofEngineTypes.Fail
+          "Rewrite: the argument is not a proof of an equality")
+   in
+    let pred =
+     let gty' = CicSubstitution.lift 1 gty in
+     let t1' = CicSubstitution.lift 1 t1 in
+     let gty'' =
+      ProofEngineReduction.replace_lifting
+       ~equality:
+        (ProofEngineReduction.syntactic_equality ~alpha_equivalence:true)
+       ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
+     in
+      C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
+    in
+prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
+    let fresh_meta = ProofEngineHelpers.new_meta proof in
+    let irl =
+     ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+    let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
+     PrimitiveTactics.exact_tac  
+      (C.Appl
+        [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
+       ((curi,metasenv',pbo,pty),goal)
+;;
+
+(******************** THE FOURIER TACTIC ***********************)
 
 (* La tactique Fourier ne fonctionne de manière sûre que si les coefficients 
 des inéquations et équations sont entiers. En attendant la tactique Field.
@@ -428,62 +479,49 @@ Construction de la preuve en cas de succ
 i.e. on obtient une contradiction.
 *)
 
-let _R = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R.con") 0 ;;
+
+let _eqT = Cic.MutInd(UriManager.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") 0 0 ;;
+let _False = Cic.MutInd (UriManager.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 0 ;;
+let _not = Cic.Const (UriManager.uri_of_string "cic:/Coq/Init/Logic/not.con") 0;;
 let _R0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R0.con") 0 ;;
 let _R1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R1.con") 0 ;;
+let _R = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R.con") 0 ;;
+let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") 0 ;;
+let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") 0 ;;
+let _Rfourier_ge_to_le  =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") 0 ;;
+let _Rfourier_gt_to_lt         =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") 0 ;;
+let _Rfourier_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") 0 ;;
+let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") 0 ;;
+let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") 0 ;;
+let _Rfourier_lt=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") 0 ;;
+let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") 0 ;;
+let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") 0 ;;
+let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") 0 ;;
+let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") 0 ;;
+let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") 0 ;;
+let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") 0 ;;
 let _Rinv  = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rinv.con") 0 ;;
+let _Rinv_R1 = Cic.Const(UriManager.uri_of_string "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) 0;;
+let _Rle = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rle.con") 0 ;;
 let _Rle_mult_inv_pos =  Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_mult_inv_pos.con") 0 ;;
 let _Rle_not_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_not_lt.con") 0 ;;
 let _Rle_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_1.con") 0 ;;
 let _Rle_zero_pos_plus1 =  Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_pos_plus1.con") 0 ;;
 let _Rle_zero_zero = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_zero.con") 0 ;;
+let _Rlt = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rlt.con") 0 ;;
 let _Rlt_mult_inv_pos = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_mult_inv_pos.con") 0 ;;
 let _Rlt_not_le =  Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_not_le.con") 0 ;;
 let _Rlt_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_1.con") 0 ;;
 let _Rlt_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_pos_plus1.con") 0 ;;
-let _Rmult = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rmult.con") 0 ;;
 let _Rminus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rminus.con") 0 ;;
-
+let _Rmult = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rmult.con") 0 ;;
+let _Rnot_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") 0 ;;
 let _Rnot_lt0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt0.con") 0 ;;
+let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") 0 ;;
 let _Ropp = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Ropp.con") 0 ;;
 let _Rplus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rplus.con") 0 ;;
-let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") 0 ;;
-let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") 0 ;;
-let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") 0 ;;
-let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") 0 ;;
-let _Rfourier_gt_to_lt         =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") 0 ;;
-
-let _Rfourier_ge_to_le  =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") 0 ;;
-let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") 0 ;;
-let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") 0 ;;
-let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") 0 ;;
-let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") 0 ;;
-
-let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") 0 ;;
-
-let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") 0 ;;
-let _Rlt = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rlt.con") 0 ;;
-let _Rle = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rle.con") 0 ;;
-let _not = Cic.Const (UriManager.uri_of_string "cic:/Coq/Init/Logic/not.con") 0;;
-
 let _sym_eqT = Cic.Const(UriManager.uri_of_string "/Coq/Init/Logic_Type/Equality_is_a_congruence/sym_eqT.con") 0 ;;
-
-let _Rfourier_lt=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") 0 ;;
-let _Rfourier_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") 0 ;;
-let _False = Cic.MutInd (UriManager.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 0 ;;
-
-let _Rinv_R1 = Cic.Const(UriManager.uri_of_string "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) 0;;
-
-
-let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") 0 ;;
-let _Rnot_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") 0 ;;
-
-
-
-
-
-
+(*****************************************************************************************************)
 let is_int x = (x.den)=1
 ;;
 
@@ -497,6 +535,7 @@ let rec rational_to_fraction x= (x.num,x.den)
 let rec int_to_real_aux n =
   match n with
     0 -> _R0 (* o forse R0 + R0 ????? *)
+  | 1 -> _R1
   | _ -> Cic.Appl [ _Rplus ; _R1 ; int_to_real_aux (n-1) ]
 ;;     
        
@@ -521,6 +560,8 @@ let rational_to_real x =
 (* preuve que 0<n*1/d
 *)
 
+
+(*
 let tac_zero_inf_pos gl (n,d) =
    (*let cste = pf_parse_constr gl in*)
    let tacn=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
@@ -530,8 +571,37 @@ let tac_zero_inf_pos gl (n,d) =
    for i=1 to d-1 do
        tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd); done;
    (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos) ~continuations:[!tacn;!tacd])
-;;
+;;*)
+let tac_zero_inf_pos (n,d) ~status =
+   (*let cste = pf_parse_constr gl in*)
+   let pall str ~status:(proof,goal) t =
+     debug ("tac "^str^" :\n" );
+     let curi,metasenv,pbo,pty = proof in
+     let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+     debug ("th = "^ CicPp.ppterm t ^"\n"); 
+     debug ("ty = "^ CicPp.ppterm ty^"\n"); 
+   in
+   let tacn=ref 
+     (fun ~status -> pall "n0" ~status _Rlt_zero_1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
+   let tacd=ref 
+     (fun ~status -> pall "d0" ~status _Rlt_zero_1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
+
+
+  for i=1 to n-1 do 
+       tacn:=(Tacticals.then_ ~start:(fun ~status -> pall ("n"^string_of_int i) ~status _Rlt_zero_pos_plus1;PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacn); done;
+   for i=1 to d-1 do
+       tacd:=(Tacticals.then_ ~start:(fun ~status -> pall "d" ~status _Rlt_zero_pos_plus1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacd); done;
+
+
+
+debug("TAC ZERO INF POS\n");
 
+(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos) 
+  ~continuations:[
+   !tacn ;
+   !tacd ] 
+  ~status)
+;;
 
 
 
@@ -570,7 +640,7 @@ let tac_zero_inf_false gl (n,d) =
 
 let tac_zero_infeq_false gl (n,d) =
      (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_not_le)
-             ~continuation:(tac_zero_inf_pos gl (-n,d)))
+             ~continuation:(tac_zero_inf_pos (-n,d)))
 ;;
 
 
@@ -615,18 +685,29 @@ let my_cut ~term:c ~status:(proof,goal)=
 
 let exact = PrimitiveTactics.exact_tac;;
 
-let tac_use h = match h.htype with
-               "Rlt" -> exact ~term:h.hname
-              |"Rle" -> exact ~term:h.hname
-              |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_gt_to_lt)
-                                ~continuation:(exact ~term:h.hname))
-              |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_ge_to_le)
-                                ~continuation:(exact ~term:h.hname))
-              |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqLR_to_le)
-                                ~continuation:(exact ~term:h.hname))
-              |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqRL_to_le)
-                                ~continuation:(exact ~term:h.hname))
-              |_->assert false
+let tac_use h ~status:(proof,goal as status) = 
+debug("Inizio TC_USE\n");
+let curi,metasenv,pbo,pty = proof in
+let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+debug ("hname = "^ CicPp.ppterm h.hname ^"\n"); 
+debug ("ty = "^ CicPp.ppterm ty^"\n"); 
+
+let res = 
+match h.htype with
+  "Rlt" -> exact ~term:h.hname ~status
+  |"Rle" -> exact ~term:h.hname ~status
+  |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_gt_to_lt)
+      ~continuation:(exact ~term:h.hname)) ~status
+  |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_ge_to_le)
+      ~continuation:(exact ~term:h.hname)) ~status
+  |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqLR_to_le)
+      ~continuation:(exact ~term:h.hname)) ~status
+  |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqRL_to_le)
+      ~continuation:(exact ~term:h.hname)) ~status
+  |_->assert false
+in
+debug("Fine TAC_USE\n");
+res
 ;;
 
 
@@ -693,23 +774,21 @@ let rec superlift c n=
  
 ;;
 
-(* fix !!!!!!!!!!  this may not work *)
 let equality_replace a b ~status =
+ let module C = Cic in
   let proof,goal = status in
   let curi,metasenv,pbo,pty = proof in
   let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
-prerr_endline ("<MY_CUT: " ^ CicPp.ppterm a ^ " <=> " ^ CicPp.ppterm b) ;
-prerr_endline ("### IN MY_CUT: ") ;
-prerr_endline ("@ " ^ CicPp.ppterm ty) ;
-List.iter (function Some (n,Cic.Decl t) -> prerr_endline ("# " ^ CicPp.ppterm t)) context ;
-prerr_endline ("##- IN MY_CUT ") ;
-let res =
-       let _eqT_ind = Cic.Const( UriManager.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con" ) 0 in
-(*CSC: codice ad-hoc per questo caso!!! Non funge in generale *)
-       PrimitiveTactics.apply_tac ~term:(Cic.Appl [_eqT_ind;_R;b;Cic.Lambda(Cic.Name "pippo",_R,Cic.Appl [_not; Cic.Appl [_Rlt;_R0;Cic.Rel 1]])]) ~status
-in
-prerr_endline "EUREKA" ;
-res
+   let a_eq_b = C.Appl [ _eqT ; _R ; a ; b ] in
+   let fresh_meta = ProofEngineHelpers.new_meta proof in
+   let irl =
+    ProofEngineHelpers.identity_relocation_list_for_metavariable context in
+   let metasenv' = (fresh_meta,context,a_eq_b)::metasenv in
+   let (proof,goals) =
+    rewrite_tac ~term:(C.Meta (fresh_meta,irl))
+     ~status:((curi,metasenv',pbo,pty),goal)
+   in
+    (proof,fresh_meta::goals)
 ;;
 
 let tcl_fail a ~status:(proof,goal) =
@@ -862,44 +941,82 @@ let rec fourier ~status:(s_proof,s_goal)=
           (* ora ho i termini che descrivono i passi di fourier per risolvere il sistema *)
        
           debug "inizio a costruire tac1\n";
+         Fourier.print_rational(c1);
          
-          let tac1=ref ( if h1.hstrict then 
-                           (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_lt)
-                                             ~continuations:[tac_use h1;tac_zero_inf_pos goal            
-                                                    (rational_to_fraction c1)])
+          let tac1=ref ( fun ~status -> 
+                       debug ("Sotto tattica t1 "^(if h1.hstrict then "strict" else "lasc")^"\n");
+                       if h1.hstrict then 
+                           (Tacticals.thens ~start:(
+                           fun ~status -> 
+                           debug ("inizio t1 strict\n");
+                           let curi,metasenv,pbo,pty = proof in
+                           let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+                           debug ("th = "^ CicPp.ppterm _Rfourier_lt ^"\n"); 
+                           debug ("ty = "^ CicPp.ppterm ty^"\n"); 
+     
+                           PrimitiveTactics.apply_tac ~term:_Rfourier_lt ~status)
+                                             ~continuations:[tac_use h1;
+                                            
+                                            tac_zero_inf_pos (rational_to_fraction c1)] ~status
+                                            
+                                            )
                          else 
                            (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le)
-                                             ~continuations:[tac_use h1;tac_zero_inf_pos  goal
-                                                    (rational_to_fraction c1)]))
+                                             ~continuations:[tac_use h1;tac_zero_inf_pos                                                 (rational_to_fraction c1)] ~status))
+                                                   
           in
           s:=h1.hstrict;
          
           List.iter (fun (h,c) -> 
                (if (!s) then 
                    (if h.hstrict then 
+                       (debug("tac1 1\n");
                        tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac 
-                                                      ~term:_Rfourier_lt_lt)
+                                                       ~term:_Rfourier_lt_lt)
                                               ~continuations:[!tac1;tac_use h;
-                                                      tac_zero_inf_pos  goal 
-                                                      (rational_to_fraction c)])
+                                                      tac_zero_inf_pos   
+                                                      (rational_to_fraction c)]))
                    else 
-                       tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac 
-                                                      ~term:_Rfourier_lt_le)
+                   (
+                       debug("tac1 2\n");
+                       Fourier.print_rational(c1);
+                       tac1:=(Tacticals.thens ~start:(
+                                       fun ~status -> 
+                                       debug("INIZIO TAC 1 2\n");
+                                       
+                                       let curi,metasenv,pbo,pty = proof in
+                                       let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
+                                       debug ("th = "^ CicPp.ppterm _Rfourier_lt_le ^"\n"); 
+                                       debug ("ty = "^ CicPp.ppterm ty^"\n"); 
+     
+                                       PrimitiveTactics.apply_tac ~term:_Rfourier_lt_le ~status
+                                                      
+                                                      )
                                               ~continuations:[!tac1;tac_use h; 
-                                                      tac_zero_inf_pos  goal
-                                                       (rational_to_fraction c)])
+                                                      
+                                                      tac_zero_inf_pos (rational_to_fraction c)
+                                                      
+                                                      ]))
                     )
                else 
                    (if h.hstrict then 
+                       (
+                       
+                       debug("tac1 3\n");
                        tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_lt)
                                               ~continuations:[!tac1;tac_use h; 
-                                                      tac_zero_inf_pos  goal
-                                                       (rational_to_fraction c)])
+                                                      tac_zero_inf_pos  
+                                                       (rational_to_fraction c)]))
                    else 
-                       tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
+                       (
+                       debug("tac1 4\n");
+                       tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
                                               ~continuations:[!tac1;tac_use h; 
-                                                      tac_zero_inf_pos  goal
-                                                       (rational_to_fraction c)])));
+                                                      tac_zero_inf_pos  
+                                                       (rational_to_fraction c)]))
+                                                      
+                                                      )
+                                                     );
              s:=(!s)||(h.hstrict))
               lutil;(*end List.iter*)
              
@@ -917,8 +1034,6 @@ let rec fourier ~status:(s_proof,s_goal)=
                        ~continuation:(Tacticals.then_ 
                                ~start:(PrimitiveTactics.apply_tac 
                                                ~term:(if sres then _Rnot_lt_lt else _Rnot_le_le))
-                                ~continuation:Ring.id_tac
-(*CSC
                                ~continuation:(Tacticals.thens 
                                                ~start:(equality_replace (Cic.Appl [_Rminus;!t2;!t1] ) tc)
                                                ~continuations:[tac2;(Tacticals.thens 
@@ -936,7 +1051,7 @@ let rec fourier ~status:(s_proof,s_goal)=
                                
                                         )
                                                ] (* end continuations before comment *)
-                                       ) *)
+                                       )
                                );
                        !tac1]
                );(*end tac:=*)
@@ -953,10 +1068,9 @@ let rec fourier ~status:(s_proof,s_goal)=
       |_-> assert false)(*match (!lutil) *)
   |_-> assert false); (*match res*)
 
-  debug ("finalmente applico t1\n");
+  debug ("finalmente applico tac\n");
   (!tac ~status:(proof,goal)) 
 
 ;;
 
 let fourier_tac ~status:(proof,goal) = fourier ~status:(proof,goal);;
-