Imported Upstream snapshot 8.3~beta0+13298

15 files changed, 0 insertions, 2643 deletions

diff --git a/contrib/dp/Dp.v b/contrib/dp/Dp.v
deleted file mode 100644
index 857c182c..00000000
--- a/contrib/dp/Dp.v
+++ /dev/null
@@ -1,120 +0,0 @@
-(* Calls to external decision procedures *)
-
-Require Export ZArith.
-Require Export Classical.
-
-(* Zenon *)
-
-(*  Copyright 2004 INRIA  *)
-(*  $Id: Dp.v 10739 2008-04-01 14:45:20Z herbelin $  *)
-
-Lemma zenon_nottrue :
-  (~True -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_noteq : forall (T : Type) (t : T),
-  ((t <> t) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_and : forall P Q : Prop,
-  (P -> Q -> False) -> (P /\ Q -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_or : forall P Q : Prop,
-  (P -> False) -> (Q -> False) -> (P \/ Q -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_imply : forall P Q : Prop,
-  (~P -> False) -> (Q -> False) -> ((P -> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_equiv : forall P Q : Prop,
-  (~P -> ~Q -> False) -> (P -> Q -> False) -> ((P <-> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notand : forall P Q : Prop,
-  (~P -> False) -> (~Q -> False) -> (~(P /\ Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notor : forall P Q : Prop,
-  (~P -> ~Q -> False) -> (~(P \/ Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notimply : forall P Q : Prop,
-  (P -> ~Q -> False) -> (~(P -> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notequiv : forall P Q : Prop,
-  (~P -> Q -> False) -> (P -> ~Q -> False) -> (~(P <-> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_ex : forall (T : Type) (P : T -> Prop),
-  (forall z : T, ((P z) -> False)) -> ((exists x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_all : forall (T : Type) (P : T -> Prop) (t : T),
-  ((P t) -> False) -> ((forall x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_notex : forall (T : Type) (P : T -> Prop) (t : T),
-  (~(P t) -> False) -> (~(exists x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_notall : forall (T : Type) (P : T -> Prop),
-  (forall z : T, (~(P z) -> False)) -> (~(forall x : T, (P x)) -> False).
-Proof. intros T P Ha Hb. apply Hb. intro. apply NNPP. exact (Ha x). Qed.
-
-Lemma zenon_equal_base : forall (T : Type) (f : T), f = f.
-Proof. auto. Qed.
-
-Lemma zenon_equal_step :
-  forall (S T : Type) (fa fb : S -> T) (a b : S),
-  (fa = fb) -> (a <> b -> False) -> ((fa a) = (fb b)).
-Proof. intros. rewrite (NNPP (a = b)). congruence. auto. Qed.
-
-Lemma zenon_pnotp : forall P Q : Prop,
-  (P = Q) -> (P -> ~Q -> False).
-Proof. intros P Q Ha. rewrite Ha. auto. Qed.
-
-Lemma zenon_notequal : forall (T : Type) (a b : T),
-  (a = b) -> (a <> b -> False).
-Proof. auto. Qed.
-
-Ltac zenon_intro id :=
-  intro id || let nid := fresh in (intro nid; clear nid)
-.
-
-Definition zenon_and_s := fun P Q a b => zenon_and P Q b a.
-Definition zenon_or_s := fun P Q a b c => zenon_or P Q b c a.
-Definition zenon_imply_s := fun P Q a b c => zenon_imply P Q b c a.
-Definition zenon_equiv_s := fun P Q a b c => zenon_equiv P Q b c a.
-Definition zenon_notand_s := fun P Q a b c => zenon_notand P Q b c a.
-Definition zenon_notor_s := fun P Q a b => zenon_notor P Q b a.
-Definition zenon_notimply_s := fun P Q a b => zenon_notimply P Q b a.
-Definition zenon_notequiv_s := fun P Q a b c => zenon_notequiv P Q b c a.
-Definition zenon_ex_s := fun T P a b => zenon_ex T P b a.
-Definition zenon_notall_s := fun T P a b => zenon_notall T P b a.
-
-Definition zenon_pnotp_s := fun P Q a b c => zenon_pnotp P Q c a b.
-Definition zenon_notequal_s := fun T a b x y => zenon_notequal T a b y x.
-
-(* Ergo *)
-
-Set Implicit Arguments.
-Section congr.
-  Variable t:Type.
-Lemma ergo_eq_concat_1 : 
-  forall (P:t -> Prop) (x y:t),
-    P x -> x = y -> P y.
-Proof.
-  intros; subst; auto.
-Qed.
-
-Lemma ergo_eq_concat_2 : 
-  forall (P:t -> t -> Prop) (x1 x2 y1 y2:t),
-    P x1 x2 -> x1 = y1 -> x2 = y2 -> P y1 y2.
-Proof.
-  intros; subst; auto.
-Qed.
-
-End congr.
diff --git a/contrib/dp/TODO b/contrib/dp/TODO
deleted file mode 100644
index 44349e21..00000000
--- a/contrib/dp/TODO
+++ /dev/null
@@ -1,24 +0,0 @@
-
-TODO
-----
-
-- axiomes pour les prédicats récursifs comme
-
-  Fixpoint even (n:nat) : Prop :=
-  match n with 
-  O => True
-  | S O => False
-  | S (S p) => even p
-  end.
-
-  ou encore In sur les listes du module Coq List.
-
-- discriminate
-
-- inversion (Set et Prop)
-
-
-BUGS
-----
-
-
diff --git a/contrib/dp/dp.ml b/contrib/dp/dp.ml
deleted file mode 100644
index d8803847..00000000
--- a/contrib/dp/dp.ml
+++ /dev/null
@@ -1,991 +0,0 @@
-(* Authors: Nicolas Ayache and Jean-Christophe Filliâtre *)
-(* Tactics to call decision procedures *)
-
-(* Works in two steps: 
-
-   - first the Coq context and the current goal are translated in
-     Polymorphic First-Order Logic (see fol.mli in this directory)
-
-   - then the resulting query is passed to the Why tool that translates
-     it to the syntax of the selected prover (Simplify, CVC Lite, haRVey,
-     Zenon)
-*)
-
-open Util
-open Pp
-open Libobject
-open Summary
-open Term
-open Tacmach
-open Tactics
-open Tacticals
-open Fol
-open Names
-open Nameops
-open Termops
-open Coqlib
-open Hipattern
-open Libnames
-open Declarations
-open Dp_why
-
-let debug = ref false
-let set_debug b = debug := b
-let trace = ref false
-let set_trace b = trace := b
-let timeout = ref 10
-let set_timeout n = timeout := n
-
-let (dp_timeout_obj,_) = 
-  declare_object 
-    {(default_object "Dp_timeout") with  
-       cache_function = (fun (_,x) -> set_timeout x);
-       load_function = (fun _ (_,x) -> set_timeout x);
-       export_function = (fun x -> Some x)}
-
-let dp_timeout x = Lib.add_anonymous_leaf (dp_timeout_obj x)
-
-let (dp_debug_obj,_) = 
-  declare_object 
-    {(default_object "Dp_debug") with  
-       cache_function = (fun (_,x) -> set_debug x);
-       load_function = (fun _ (_,x) -> set_debug x);
-       export_function = (fun x -> Some x)}
-
-let dp_debug x = Lib.add_anonymous_leaf (dp_debug_obj x)
-
-let (dp_trace_obj,_) = 
-  declare_object 
-    {(default_object "Dp_trace") with  
-       cache_function = (fun (_,x) -> set_trace x);
-       load_function = (fun _ (_,x) -> set_trace x);
-       export_function = (fun x -> Some x)}
-
-let dp_trace x = Lib.add_anonymous_leaf (dp_trace_obj x)
-
-let logic_dir = ["Coq";"Logic";"Decidable"]
-let coq_modules =
-  init_modules @ [logic_dir] @ arith_modules @ zarith_base_modules
-    @ [["Coq"; "ZArith"; "BinInt"]]
-    @ [["Coq"; "omega"; "OmegaLemmas"]]
-
-let constant = gen_constant_in_modules "dp" coq_modules
-
-let coq_Z = lazy (constant "Z")
-let coq_Zplus = lazy (constant "Zplus")
-let coq_Zmult = lazy (constant "Zmult")
-let coq_Zopp = lazy (constant "Zopp")
-let coq_Zminus = lazy (constant "Zminus")
-let coq_Zdiv = lazy (constant "Zdiv")
-let coq_Zs = lazy (constant "Zs")
-let coq_Zgt = lazy (constant "Zgt")
-let coq_Zle = lazy (constant "Zle")
-let coq_Zge = lazy (constant "Zge")
-let coq_Zlt = lazy (constant "Zlt")
-let coq_Z0 = lazy (constant "Z0")
-let coq_Zpos = lazy (constant "Zpos")
-let coq_Zneg = lazy (constant "Zneg")
-let coq_xH = lazy (constant "xH")
-let coq_xI = lazy (constant "xI")
-let coq_xO = lazy (constant "xO")
-let coq_iff = lazy (constant "iff")
-
-(* not Prop typed expressions *)
-exception NotProp
-
-(* not first-order expressions *)
-exception NotFO
-
-(* Renaming of Coq globals *)
-
-let global_names = Hashtbl.create 97
-let used_names = Hashtbl.create 97
-
-let rename_global r =
-  try 
-    Hashtbl.find global_names r
-  with Not_found ->
-    let rec loop id = 
-      if Hashtbl.mem used_names id then 
-	loop (lift_ident id)
-      else begin 
-	Hashtbl.add used_names id ();
-	let s = string_of_id id in
-	Hashtbl.add global_names r s; 
-	s
-      end
-    in
-    loop (Nametab.id_of_global r)
-
-let foralls =
-  List.fold_right 
-    (fun (x,t) p -> Forall (x, t, p))
-
-let fresh_var = function
-  | Anonymous -> rename_global (VarRef (id_of_string "x"))
-  | Name x -> rename_global (VarRef x)
-
-(* coq_rename_vars env [(x1,t1);...;(xn,tn)] renames the xi outside of 
-   env names, and returns the new variables together with the new 
-   environment *)
-let coq_rename_vars env vars =
-  let avoid = ref (ids_of_named_context (Environ.named_context env)) in
-  List.fold_right
-    (fun (na,t) (newvars, newenv) -> 
-       let id = next_name_away na !avoid in
-       avoid := id :: !avoid;
-       id :: newvars, Environ.push_named (id, None, t) newenv)
-    vars ([],env)
-
-(* extract the prenex type quantifications i.e.
-   type_quantifiers env (A1:Set)...(Ak:Set)t = A1...An, (env+Ai), t *)
-let decomp_type_quantifiers env t =
-  let rec loop vars t = match kind_of_term t with
-    | Prod (n, a, t) when is_Set a || is_Type a -> 
-	loop ((n,a) :: vars) t
-    | _ -> 
-	let vars, env = coq_rename_vars env vars in
-	let t = substl (List.map mkVar vars) t in
-	List.rev vars, env, t
-  in
-  loop [] t
-
-(* same thing with lambda binders (for axiomatize body) *)
-let decomp_type_lambdas env t =
-  let rec loop vars t = match kind_of_term t with
-    | Lambda (n, a, t) when is_Set a || is_Type a -> 
-	loop ((n,a) :: vars) t
-    | _ -> 
-	let vars, env = coq_rename_vars env vars in
-	let t = substl (List.map mkVar vars) t in
-	List.rev vars, env, t
-  in
-  loop [] t
-
-let decompose_arrows = 
-  let rec arrows_rec l c = match kind_of_term c with
-    | Prod (_,t,c) when not (dependent (mkRel 1) c) -> arrows_rec (t :: l) c
-    | Cast (c,_,_) -> arrows_rec l c
-    | _ -> List.rev l, c
-  in 
-  arrows_rec []
-
-let rec eta_expanse t vars env i =
-  assert (i >= 0);
-  if i = 0 then
-    t, vars, env
-  else
-    match kind_of_term (Typing.type_of env Evd.empty t) with
-      | Prod (n, a, b) when not (dependent (mkRel 1) b) ->
-	  let avoid = ids_of_named_context (Environ.named_context env) in
-	  let id = next_name_away n avoid in
-	  let env' = Environ.push_named (id, None, a) env in
-	  let t' = mkApp (t, [| mkVar id |]) in
-	  eta_expanse t' (id :: vars) env' (pred i)
-      | _ -> 
-	  assert false
-
-let rec skip_k_args k cl = match k, cl with
-  | 0, _ -> cl
-  | _, _ :: cl -> skip_k_args (k-1) cl
-  | _, [] -> raise NotFO
-
-(* Coq global references *)
-
-type global = Gnot_fo | Gfo of Fol.decl
-
-let globals = ref Refmap.empty
-let globals_stack = ref []
-
-(* synchronization *)
-let () =
-  Summary.declare_summary "Dp globals"
-    { Summary.freeze_function = (fun () -> !globals, !globals_stack);
-      Summary.unfreeze_function = 
-	(fun (g,s) -> globals := g; globals_stack := s);
-      Summary.init_function = (fun () -> ());
-      Summary.survive_module = false;
-      Summary.survive_section = false }
-
-let add_global r d = globals := Refmap.add r d !globals
-let mem_global r = Refmap.mem r !globals
-let lookup_global r = match Refmap.find r !globals with
-  | Gnot_fo -> raise NotFO
-  | Gfo d -> d
-
-let locals = Hashtbl.create 97
-
-let lookup_local r =  match Hashtbl.find locals r with
-  | Gnot_fo -> raise NotFO
-  | Gfo d -> d
-
-let iter_all_constructors i f =  
-  let _, oib = Global.lookup_inductive i in
-  Array.iteri
-    (fun j tj -> f j (mkConstruct (i, j+1)))
-    oib.mind_nf_lc
-
-
-(* injection c [t1,...,tn] adds the injection axiom
-     forall x1:t1,...,xn:tn,y1:t1,...,yn:tn. 
-       c(x1,...,xn)=c(y1,...,yn) -> x1=y1 /\ ... /\ xn=yn *)
-
-let injection c l =
-  let i = ref 0 in
-  let var s = incr i; id_of_string (s ^ string_of_int !i) in
-  let xl = List.map (fun t -> rename_global (VarRef (var "x")), t) l in
-  i := 0;
-  let yl = List.map (fun t -> rename_global (VarRef (var "y")), t) l in
-  let f = 
-    List.fold_right2 
-      (fun (x,_) (y,_) p -> And (Fatom (Eq (App (x,[]),App (y,[]))), p))
-      xl yl True
-  in
-  let vars = List.map (fun (x,_) -> App(x,[])) in
-  let f = Imp (Fatom (Eq (App (c, vars xl), App (c, vars yl))), f) in
-  let foralls = List.fold_right (fun (x,t) p -> Forall (x, t, p)) in
-  let f = foralls xl (foralls yl f) in
-  let ax = Axiom ("injection_" ^ c, f) in
-  globals_stack := ax :: !globals_stack
-
-(* rec_names_for c [|n1;...;nk|] builds the list of constant names for 
-   identifiers n1...nk with the same path as c, if they exist; otherwise
-   raises Not_found *)
-let rec_names_for c =
-  let mp,dp,_ = Names.repr_con c in
-  array_map_to_list
-    (function 
-       | Name id -> 
-	   let c' = Names.make_con mp dp (label_of_id id) in
-	   ignore (Global.lookup_constant c');
-	   msgnl (Printer.pr_constr (mkConst c'));
-	   c'
-       | Anonymous ->
-	   raise Not_found)
-
-(* abstraction tables *)
-
-let term_abstractions = Hashtbl.create 97
-
-let new_abstraction = 
-  let r = ref 0 in fun () -> incr r; "abstraction_" ^ string_of_int !r
-
-(* Arithmetic constants *)
-
-exception NotArithConstant
-
-(* translates a closed Coq term p:positive into a FOL term of type int *)
-let rec tr_positive p = match kind_of_term p with
-  | Term.Construct _ when p = Lazy.force coq_xH ->
-      Cst 1
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xI ->
-      Plus (Mult (Cst 2, tr_positive a), Cst 1)
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xO ->
-      Mult (Cst 2, tr_positive a)
-  | Term.Cast (p, _, _) ->
-      tr_positive p
-  | _ ->
-      raise NotArithConstant
-
-(* translates a closed Coq term t:Z into a FOL term of type int *)
-let rec tr_arith_constant t = match kind_of_term t with
-  | Term.Construct _ when t = Lazy.force coq_Z0 ->
-      Cst 0
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zpos ->
-      tr_positive a
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zneg ->
-      Moins (Cst 0, tr_positive a)
-  | Term.Cast (t, _, _) ->
-      tr_arith_constant t
-  | _ -> 
-      raise NotArithConstant
-
-(* translate a Coq term t:Set into a FOL type expression;
-   tv = list of type variables *)
-and tr_type tv env t =
-  let t = Reductionops.nf_betadeltaiota env Evd.empty t in
-  if t = Lazy.force coq_Z then 
-    Tid ("int", [])
-  else match kind_of_term t with
-    | Var x when List.mem x tv ->
-	Tvar (string_of_id x)
-    | _ ->
-	let f, cl = decompose_app t in
-	begin try
-	  let r = global_of_constr f in
-	  match tr_global env r with
-	    | DeclType (id, k) -> 
-		assert (k = List.length cl); (* since t:Set *)
-		Tid (id, List.map (tr_type tv env) cl)
-	    | _ -> 
-		raise NotFO
-	with 
-	  | Not_found ->
-	      raise NotFO
-	  | NotFO -> 
-	      (* we need to abstract some part of (f cl) *)
-	      (*TODO*)
-	      raise NotFO
-	end
-
-and make_term_abstraction tv env c =
-  let ty = Typing.type_of env Evd.empty c in
-  let id = new_abstraction () in
-  match tr_decl env id ty with
-    | DeclFun (id,_,_,_) as d ->
-	begin try
-	  Hashtbl.find term_abstractions c
-	with Not_found ->
-	  Hashtbl.add term_abstractions c id;
-	  globals_stack := d :: !globals_stack;
-	  id
-	end
-    | _ ->
-	raise NotFO
-
-(* translate a Coq declaration id:ty in a FOL declaration, that is either
-   - a type declaration : DeclType (id, n) where n:int is the type arity
-   - a function declaration : DeclFun (id, tl, t) ; that includes constants
-   - a predicate declaration : DeclPred (id, tl)
-   - an axiom : Axiom (id, p)
- *)
-and tr_decl env id ty =
-  let tv, env, t = decomp_type_quantifiers env ty in
-  if is_Set t || is_Type t then
-    DeclType (id, List.length tv)
-  else if is_Prop t then
-    DeclPred (id, List.length tv, [])
-  else 
-    let s = Typing.type_of env Evd.empty t in
-    if is_Prop s then
-      Axiom (id, tr_formula tv [] env t)
-    else
-      let l, t = decompose_arrows t in
-      let l = List.map (tr_type tv env) l in
-      if is_Prop t then
-	DeclPred(id, List.length tv, l)
-      else 
-	let s = Typing.type_of env Evd.empty t in
-	if is_Set s || is_Type s then 
-	  DeclFun (id, List.length tv, l, tr_type tv env t)
-	else 
-	  raise NotFO
-
-(* tr_global(r) = tr_decl(id(r),typeof(r)) + a cache mechanism *)
-and tr_global env r = match r with
-  | VarRef id ->
-      lookup_local id
-  | r ->
-      try
-	lookup_global r
-      with Not_found ->
-	try
-	  let ty = Global.type_of_global r in
-	  let id = rename_global r in
-	  let d = tr_decl env id ty in
-	  (* r can be already declared if it is a constructor *)
-	  if not (mem_global r) then begin 
-	    add_global r (Gfo d);
-	    globals_stack := d :: !globals_stack
-	  end;
-	  begin try axiomatize_body env r id d with NotFO -> () end;
-	  d
-	with NotFO ->
-	  add_global r Gnot_fo;
-	  raise NotFO
-
-and axiomatize_body env r id d = match r with
-  | VarRef _ -> 
-      assert false
-  | ConstRef c ->
-      begin match (Global.lookup_constant c).const_body with
-	| Some b ->
-	    let b = force b in
-	    let axioms =
-	      (match d with
-		 | DeclPred (id, _, []) ->
-		     let tv, env, b = decomp_type_lambdas env b in
-		     let value = tr_formula tv [] env b in
-		     [id, Iff (Fatom (Pred (id, [])), value)]
-		 | DeclFun (id, _, [], _) ->
-		     let tv, env, b = decomp_type_lambdas env b in
-		     let value = tr_term tv [] env b in
-		     [id, Fatom (Eq (Fol.App (id, []), value))]
-		 | DeclFun (id, _, l, _) | DeclPred (id, _, l) ->
-		     (*Format.eprintf "axiomatize_body %S@." id;*)
-		     let b = match kind_of_term b with
-		       (* a single recursive function *)
-		       | Fix (_, (_,_,[|b|])) -> 
-			   subst1 (mkConst c) b
-                       (* mutually recursive functions *)
-		       | Fix ((_,i), (names,_,bodies)) ->
-                           (* we only deal with named functions *)
-			   begin try
-			     let l = rec_names_for c names in
-			     substl (List.rev_map mkConst l) bodies.(i)
-			   with Not_found ->
-			     b
-			   end
-		       | _ -> 
-			   b
-		     in
-		     let tv, env, b = decomp_type_lambdas env b in
-		     let vars, t = decompose_lam b in
-		     let n = List.length l in
-		     let k = List.length vars in
-		     assert (k <= n);
-		     let vars, env = coq_rename_vars env vars in
-		     let t = substl (List.map mkVar vars) t in
-		     let t, vars, env = eta_expanse t vars env (n-k) in
-		     let vars = List.rev vars in
-		     let bv = vars in
-		     let vars = List.map (fun x -> string_of_id x) vars in
-		     let fol_var x = Fol.App (x, []) in
-		     let fol_vars = List.map fol_var vars in
-		     let vars = List.combine vars l in
-		     begin match d with
-		       | DeclFun (_, _, _, ty) ->
-			   begin match kind_of_term t with
-			     | Case (ci, _, e, br) ->
-				 equations_for_case env id vars tv bv ci e br
-			     | _ -> 
-				 let t = tr_term tv bv env t in
-				 let ax = 
-				   add_proof (Fun_def (id, vars, ty, t))
-				 in
-				 let p = Fatom (Eq (App (id, fol_vars), t)) in
-				 [ax, foralls vars p]
-			   end
-		       | DeclPred _ ->
-			   let value = tr_formula tv bv env t in
-			   let p = Iff (Fatom (Pred (id, fol_vars)), value) in
-			   [id, foralls vars p]
-		       | _ ->
-			   assert false
-		     end
-		 | DeclType _ ->
-		     raise NotFO
-		 | Axiom _ -> assert false)
-	    in
-	    let axioms = List.map (fun (id,ax) -> Axiom (id, ax)) axioms in
-	    globals_stack := axioms @ !globals_stack
-	| None -> 
-	    () (* Coq axiom *)
-      end
-  | IndRef i ->
-      iter_all_constructors i
-	(fun _ c ->
-	   let rc = global_of_constr c in
-	   try
-	     begin match tr_global env rc with
-	       | DeclFun (_, _, [], _) -> ()
-	       | DeclFun (idc, _, al, _) -> injection idc al
-	       | _ -> ()
-	     end
-	   with NotFO ->
-	     ())
-  | _ -> ()
-
-and equations_for_case env id vars tv bv ci e br = match kind_of_term e with
-  | Var x when List.exists (fun (y, _) -> string_of_id x = y) vars ->
-      let eqs = ref [] in
-      iter_all_constructors ci.ci_ind
-	(fun j cj ->
-	   try
-	     let cjr = global_of_constr cj in
-	     begin match tr_global env cjr with
-	       | DeclFun (idc, _, l, _) ->
-		   let b = br.(j) in
-		   let rec_vars, b = decompose_lam b in
-		   let rec_vars, env = coq_rename_vars env rec_vars in
-		   let coq_rec_vars = List.map mkVar rec_vars in
-		   let b = substl coq_rec_vars b in
-		   let rec_vars = List.rev rec_vars in
-		   let coq_rec_term = applist (cj, List.rev coq_rec_vars) in
-		   let b = replace_vars [x, coq_rec_term] b in
-		   let bv = bv @ rec_vars in
-		   let rec_vars = List.map string_of_id rec_vars in
-		   let fol_var x = Fol.App (x, []) in
-		   let fol_rec_vars = List.map fol_var rec_vars in
-		   let fol_rec_term = App (idc, fol_rec_vars) in
-		   let rec_vars = List.combine rec_vars l in
-		   let fol_vars = List.map fst vars in
-		   let fol_vars = List.map fol_var fol_vars in
-		   let fol_vars = List.map (fun y -> match y with
-					      | App (id, _) ->
-						  if id = string_of_id x
-						  then fol_rec_term
-						  else y
-					      | _ -> y)
-				    fol_vars in
-		   let vars = vars @ rec_vars in
-		   let rec remove l e = match l with
-		     | [] -> []
-		     | (y, t)::l' -> if y = string_of_id e then l'
-		       else (y, t)::(remove l' e) in
-		   let vars = remove vars x in
-		   let p = 
-		     Fatom (Eq (App (id, fol_vars), 
-				tr_term tv bv env b))
-		   in
-		   eqs := (id ^ "_" ^ idc, foralls vars p) :: !eqs
-	       | _ -> 
-		   assert false end
-	   with NotFO ->
-	     ());
-      !eqs
-  | _ ->
-      raise NotFO
-
-(* assumption: t:T:Set *)
-and tr_term tv bv env t = match kind_of_term t with
-  | Term.App (f, [|a;b|]) when f = Lazy.force coq_Zplus -> 
-      Plus (tr_term tv bv env a, tr_term tv bv env b)
-  | Term.App (f, [|a;b|]) when f = Lazy.force coq_Zminus -> 
-      Moins (tr_term tv bv env a, tr_term tv bv env b)
-  | Term.App (f, [|a;b|]) when f = Lazy.force coq_Zmult -> 
-      Mult (tr_term tv bv env a, tr_term tv bv env b)
-  | Term.App (f, [|a;b|]) when f = Lazy.force coq_Zdiv -> 
-      Div (tr_term tv bv env a, tr_term tv bv env b)
-  | Term.Var id when List.mem id bv ->
-      App (string_of_id id, [])
-  | _ ->
-      try
-	tr_arith_constant t
-      with NotArithConstant ->
-	let f, cl = decompose_app t in
-	begin try
-	  let r = global_of_constr f in
-	  match tr_global env r with
-	    | DeclFun (s, k, _, _) -> 
-		let cl = skip_k_args k cl in
-		Fol.App (s, List.map (tr_term tv bv env) cl)
-	    | _ -> 
-		raise NotFO
-	with 
-	  | Not_found ->
-	      raise NotFO
-	  | NotFO -> (* we need to abstract some part of (f cl) *)
-	      let rec abstract app = function
-		| [] ->
-		    Fol.App (make_term_abstraction tv env app, [])
-		| x :: l as args ->
-		    begin try
-		      let s = make_term_abstraction tv env app in
-		      Fol.App (s, List.map (tr_term tv bv env) args)
-		    with NotFO ->
-		      abstract (applist (app, [x])) l
-		    end
-	      in
-	      let app,l = match cl with 
-		| x :: l -> applist (f, [x]), l | [] -> raise NotFO
-	      in
-	      abstract app l
-	end
-
-and quantifiers n a b tv bv env =
-  let vars, env = coq_rename_vars env [n,a] in
-  let id = match vars with [x] -> x | _ -> assert false in
-  let b = subst1 (mkVar id) b in
-  let t = tr_type tv env a in
-  let bv = id :: bv in
-  id, t, bv, env, b
-
-(* assumption: f is of type Prop *)
-and tr_formula tv bv env f =
-  let c, args = decompose_app f in
-  match kind_of_term c, args with
-    | Var id, [] -> 
-	Fatom (Pred (rename_global (VarRef id), []))
-    | _, [t;a;b] when c = build_coq_eq () ->
-	let ty = Typing.type_of env Evd.empty t in
-	if is_Set ty || is_Type ty then
-	  let _ = tr_type tv env t in
-	  Fatom (Eq (tr_term tv bv env a, tr_term tv bv env b))
-	else 
-	  raise NotFO
-    | _, [a;b] when c = Lazy.force coq_Zle ->
-	Fatom (Le (tr_term tv bv env a, tr_term tv bv env b))
-    | _, [a;b] when c = Lazy.force coq_Zlt ->
-	Fatom (Lt (tr_term tv bv env a, tr_term tv bv env b))
-    | _, [a;b] when c = Lazy.force coq_Zge ->
-	Fatom (Ge (tr_term tv bv env a, tr_term tv bv env b))
-    | _, [a;b] when c = Lazy.force coq_Zgt ->
-	Fatom (Gt (tr_term tv bv env a, tr_term tv bv env b))
-    | _, [] when c = build_coq_False () ->
-	False
-    | _, [] when c = build_coq_True () ->
-	True
-    | _, [a] when c = build_coq_not () ->
-	Not (tr_formula tv bv env a)
-    | _, [a;b] when c = build_coq_and () ->
-	And (tr_formula tv bv env a, tr_formula tv bv env b)
-    | _, [a;b] when c = build_coq_or () ->
-	Or (tr_formula tv bv env a, tr_formula tv bv env b)
-    | _, [a;b] when c = Lazy.force coq_iff ->
-	Iff (tr_formula tv bv env a, tr_formula tv bv env b)
-    | Prod (n, a, b), _ ->
-	if is_imp_term f then
-	  Imp (tr_formula tv bv env a, tr_formula tv bv env b)
-	else
-	  let id, t, bv, env, b = quantifiers n a b tv bv env in
-	  Forall (string_of_id id, t, tr_formula tv bv env b)
-    | _, [_; a] when c = build_coq_ex () ->
-	begin match kind_of_term a with
-	  | Lambda(n, a, b) ->
-	      let id, t, bv, env, b = quantifiers n a b tv bv env in
-	      Exists (string_of_id id, t, tr_formula tv bv env b)
-	  | _ -> 
-	      (* unusual case of the shape (ex p) *)
-	      raise NotFO (* TODO: we could eta-expanse *)
-	end
-    | _ ->
-	begin try
-	  let r = global_of_constr c in
-	  match tr_global env r with
-	    | DeclPred (s, k, _) -> 
-		let args = skip_k_args k args in
-		Fatom (Pred (s, List.map (tr_term tv bv env) args))
-	    | _ -> 
-		raise NotFO
-	with Not_found ->
-	  raise NotFO
-	end
-
-
-let tr_goal gl =
-  Hashtbl.clear locals;
-  let tr_one_hyp (id, ty) = 
-    try
-      let s = rename_global (VarRef id) in
-      let d = tr_decl (pf_env gl) s ty in
-      Hashtbl.add locals id (Gfo d);
-      d
-    with NotFO ->
-      Hashtbl.add locals id Gnot_fo;
-      raise NotFO
-  in
-  let hyps =
-    List.fold_right 
-      (fun h acc -> try tr_one_hyp h :: acc with NotFO -> acc)
-      (pf_hyps_types gl) []
-  in
-  let c = tr_formula [] [] (pf_env gl) (pf_concl gl) in
-  let hyps = List.rev_append !globals_stack (List.rev hyps) in
-  hyps, c
-
-
-type prover = Simplify | Ergo | Yices | CVCLite | Harvey | Zenon | Gwhy
-
-let remove_files = List.iter (fun f -> try Sys.remove f with _ -> ())
-
-let sprintf = Format.sprintf
-
-let file_contents f =
-  let buf = Buffer.create 1024 in
-  try
-    let c = open_in f in
-    begin try 
-      while true do 
-	let s = input_line c in Buffer.add_string buf s; 
-	Buffer.add_char buf '\n'
-      done;
-      assert false
-    with End_of_file ->
-      close_in c;
-      Buffer.contents buf
-    end
-  with _ -> 
-    sprintf "(cannot open %s)" f
-
-let timeout_sys_command cmd =
-  if !debug then Format.eprintf "command line: %s@." cmd;
-  let out = Filename.temp_file "out" "" in
-  let cmd = sprintf "why-cpulimit %d %s > %s 2>&1" !timeout cmd out in
-  let ret = Sys.command cmd in
-  if !debug then 
-    Format.eprintf "Output file %s:@.%s@." out (file_contents out);
-  ret, out
-
-let timeout_or_failure c cmd out =
-  if c = 152 then 
-    Timeout 
-  else
-    Failure 
-      (sprintf "command %s failed with output:\n%s " cmd (file_contents out))
-
-let prelude_files = ref ([] : string list)
-
-let set_prelude l = prelude_files := l
-
-let (dp_prelude_obj,_) = 
-  declare_object 
-    {(default_object "Dp_prelude") with  
-       cache_function = (fun (_,x) -> set_prelude x);
-       load_function = (fun _ (_,x) -> set_prelude x);
-       export_function = (fun x -> Some x)}
-
-let dp_prelude x = Lib.add_anonymous_leaf (dp_prelude_obj x)
-
-let why_files f = String.concat " " (!prelude_files @ [f])
-
-let call_simplify fwhy =
-  let cmd = 
-    sprintf "why --simplify %s" (why_files fwhy)
-  in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let fsx = Filename.chop_suffix fwhy ".why" ^ "_why.sx" in
-  let cmd = 
-    sprintf "why-cpulimit %d Simplify %s > out 2>&1 && grep -q -w Valid out"
-      !timeout fsx
-  in
-  let out = Sys.command cmd in
-  let r = 
-    if out = 0 then Valid None else if out = 1 then Invalid else Timeout 
-  in
-  if not !debug then remove_files [fwhy; fsx];
-  r
-
-let call_ergo fwhy =
-  let cmd = sprintf "why --alt-ergo %s" (why_files fwhy) in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let fwhy = Filename.chop_suffix fwhy ".why" ^ "_why.why" in
-  let ftrace = Filename.temp_file "ergo_trace" "" in
-  let cmd = 
-    if !trace then
-      sprintf "ergo -cctrace %s %s" ftrace fwhy
-    else
-      sprintf "ergo %s" fwhy
-  in
-  let ret,out = timeout_sys_command cmd in
-  let r = 
-    if ret <> 0 then 
-      timeout_or_failure ret cmd out
-    else if Sys.command (sprintf "grep -q -w Valid %s" out) = 0 then
-      Valid (if !trace then Some ftrace else None)
-    else if Sys.command (sprintf "grep -q -w \"I don't know\" %s" out) = 0 then
-      DontKnow
-    else if Sys.command (sprintf "grep -q -w \"Invalid\" %s" out) = 0 then
-      Invalid
-    else
-      Failure ("command failed: " ^ cmd)
-  in
-  if not !debug then remove_files [fwhy; out];
-  r
-
-let call_zenon fwhy =
-  let cmd = 
-    sprintf "why --no-prelude --no-zenon-prelude --zenon %s" (why_files fwhy)
-  in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let fznn = Filename.chop_suffix fwhy ".why" ^ "_why.znn" in
-  let out = Filename.temp_file "dp_out" "" in
-  let cmd = 
-    sprintf "timeout %d zenon -ocoqterm %s > %s 2>&1" !timeout fznn out 
-  in
-  let c = Sys.command cmd in
-  if not !debug then remove_files [fwhy; fznn];
-  if c = 137 then 
-    Timeout
-  else begin
-    if c <> 0 then anomaly ("command failed: " ^ cmd);
-    if Sys.command (sprintf "grep -q -w Error %s" out) = 0 then
-      error "Zenon failed";
-    let c = Sys.command (sprintf "grep -q PROOF-FOUND %s" out) in
-    if c = 0 then Valid (Some out) else Invalid
-  end
-
-let call_yices fwhy =
-  let cmd = 
-    sprintf "why -smtlib --encoding sstrat %s" (why_files fwhy)
-  in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let fsmt = Filename.chop_suffix fwhy ".why" ^ "_why.smt" in
-  let cmd = 
-    sprintf "why-cpulimit %d yices -pc 0 -smt %s > out 2>&1 && grep -q -w unsat out"
-      !timeout fsmt
-  in
-  let out = Sys.command cmd in
-  let r = 
-    if out = 0 then Valid None else if out = 1 then Invalid else Timeout 
-  in
-  if not !debug then remove_files [fwhy; fsmt];
-  r
-
-let call_cvcl fwhy =
-  let cmd = 
-    sprintf "why --cvcl --encoding sstrat %s" (why_files fwhy)
-  in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let fcvc = Filename.chop_suffix fwhy ".why" ^ "_why.cvc" in
-  let cmd = 
-    sprintf "timeout %d cvcl < %s > out 2>&1 && grep -q -w Valid out" 
-      !timeout fcvc
-  in
-  let out = Sys.command cmd in
-  let r = 
-    if out = 0 then Valid None else if out = 1 then Invalid else Timeout 
-  in
-  if not !debug then remove_files [fwhy; fcvc];
-  r
-
-let call_harvey fwhy =
-  let cmd = 
-    sprintf "why --harvey --encoding strat %s" (why_files fwhy)
-  in
-  if Sys.command cmd <> 0 then error ("call to " ^ cmd ^ " failed");
-  let frv = Filename.chop_suffix fwhy ".why" ^ "_why.rv" in
-  let out = Sys.command (sprintf "rvc -e -t %s > /dev/null 2>&1" frv) in
-  if out <> 0 then anomaly ("call to rvc -e -t " ^ frv ^ " failed");
-  let f = Filename.chop_suffix frv ".rv" ^ "-0.baf" in
-  let outf = Filename.temp_file "rv" ".out" in
-  let out = 
-    Sys.command (sprintf "timeout %d rv -e\"-T 2000\" %s > %s 2>&1" 
-		   !timeout f outf) 
-  in
-  let r =
-    if out <> 0 then 
-      Timeout
-    else
-      let cmd = 
-	sprintf "grep \"Proof obligation in\" %s | grep -q \"is valid\"" outf
-      in
-      if Sys.command cmd = 0 then Valid None else Invalid
-  in
-  if not !debug then remove_files [fwhy; frv; outf];
-  r
-
-let call_gwhy fwhy =
-  let cmd = sprintf "gwhy %s" (why_files fwhy) in
-  if Sys.command cmd <> 0 then ignore (Sys.command (sprintf "emacs %s" fwhy));
-  NoAnswer
-
-let ergo_proof_from_file f gl =
-  let s =
-    let buf = Buffer.create 1024 in
-    let c = open_in f in
-    try
-      while true do Buffer.add_string buf (input_line c) done; assert false
-    with End_of_file ->
-      close_in c;
-      Buffer.contents buf
-  in
-  let parsed_constr = Pcoq.parse_string Pcoq.Constr.constr s in
-  let t = Constrintern.interp_constr (project gl) (pf_env gl) parsed_constr in
-  exact_check t gl
-
-let call_prover prover q =
-  let fwhy = Filename.temp_file "coq_dp" ".why" in
-  Dp_why.output_file fwhy q;
-  match prover with
-    | Simplify -> call_simplify fwhy
-    | Ergo -> call_ergo fwhy
-    | Yices -> call_yices fwhy
-    | Zenon -> call_zenon fwhy
-    | CVCLite -> call_cvcl fwhy
-    | Harvey -> call_harvey fwhy
-    | Gwhy -> call_gwhy fwhy
-  
-let dp prover gl =
-  Coqlib.check_required_library ["Coq";"ZArith";"ZArith"];
-  let concl_type = pf_type_of gl (pf_concl gl) in
-  if not (is_Prop concl_type) then error "Conclusion is not a Prop";
-  try 
-    let q = tr_goal gl in
-    begin match call_prover prover q with
-      | Valid (Some f) when prover = Zenon -> Dp_zenon.proof_from_file f gl
-      | Valid (Some f) when prover = Ergo -> ergo_proof_from_file f gl
-      | Valid _ -> Tactics.admit_as_an_axiom gl
-      | Invalid -> error "Invalid"
-      | DontKnow -> error "Don't know"
-      | Timeout -> error "Timeout"
-      | Failure s -> error s
-      | NoAnswer -> Tacticals.tclIDTAC gl
-    end
-  with NotFO ->
-    error "Not a first order goal"
-      
-
-let simplify = tclTHEN intros (dp Simplify)
-let ergo = tclTHEN intros (dp Ergo)
-let yices = tclTHEN intros (dp Yices)
-let cvc_lite = tclTHEN intros (dp CVCLite)
-let harvey = dp Harvey
-let zenon = tclTHEN intros (dp Zenon)
-let gwhy = tclTHEN intros (dp Gwhy)
-
-let dp_hint l =
-  let env = Global.env () in
-  let one_hint (qid,r) = 
-    if not (mem_global r) then begin
-      let ty = Global.type_of_global r in
-      let s = Typing.type_of env Evd.empty ty in
-      if is_Prop s then
-	try
-	  let id = rename_global r in
-	  let tv, env, ty = decomp_type_quantifiers env ty in
-	  let d = Axiom (id, tr_formula tv [] env ty) in
-	  add_global r (Gfo d);
-	  globals_stack := d :: !globals_stack
-	with NotFO ->
-	  add_global r Gnot_fo;
-	  msg_warning
-	    (pr_reference qid ++ 
-	     str " ignored (not a first order proposition)")
-	else begin
-	  add_global r Gnot_fo;
-	  msg_warning
-	    (pr_reference qid ++ str " ignored (not a proposition)")
-	end
-    end
-  in
-  List.iter one_hint (List.map (fun qid -> qid, Nametab.global qid) l)
-
-let (dp_hint_obj,_) = 
-  declare_object 
-    {(default_object "Dp_hint") with  
-       cache_function = (fun (_,l) -> dp_hint l);
-       load_function = (fun _ (_,l) -> dp_hint l);
-       export_function = (fun x -> Some x)}
-
-let dp_hint l = Lib.add_anonymous_leaf (dp_hint_obj l)
-
-let dp_predefined qid s =
-  let r = Nametab.global qid in
-  let ty = Global.type_of_global r in
-  let env = Global.env () in
-  let id = rename_global r in
-  try
-    let d = match tr_decl env id ty with
-      | DeclType (_, n) -> DeclType (s, n)
-      | DeclFun (_, n, tyl, ty) -> DeclFun (s, n, tyl, ty)
-      | DeclPred (_, n, tyl) -> DeclPred (s, n, tyl) 
-      | Axiom _ as d -> d
-    in
-    match d with
-      | Axiom _ ->  msg_warning (str " ignored (axiom)")
-      | d -> add_global r (Gfo d)
-  with NotFO ->
-    msg_warning (str " ignored (not a first order declaration)")
-
-let (dp_predefined_obj,_) = 
-  declare_object 
-    {(default_object "Dp_predefined") with  
-       cache_function = (fun (_,(id,s)) -> dp_predefined id s);
-       load_function = (fun _ (_,(id,s)) -> dp_predefined id s);
-       export_function = (fun x -> Some x)}
-
-let dp_predefined id s = Lib.add_anonymous_leaf (dp_predefined_obj (id,s))
-
-let _ = declare_summary "Dp options" 
-	  { freeze_function = 
-	      (fun () -> !debug, !trace, !timeout, !prelude_files);
-	    unfreeze_function = 
-	      (fun (d,tr,tm,pr) -> 
-		debug := d; trace := tr; timeout := tm; prelude_files := pr);
-	    init_function = 
-	      (fun () -> 
-		debug := false; trace := false; timeout := 10; 
-		prelude_files := []);
-	    survive_module = true;
-	    survive_section = true }  
diff --git a/contrib/dp/dp.mli b/contrib/dp/dp.mli
deleted file mode 100644
index 6dbc05e1..00000000
--- a/contrib/dp/dp.mli
+++ /dev/null
@@ -1,20 +0,0 @@
-
-open Libnames
-open Proof_type
-
-val simplify : tactic
-val ergo : tactic
-val yices : tactic
-val cvc_lite : tactic
-val harvey : tactic
-val zenon : tactic
-val gwhy : tactic
-
-val dp_hint : reference list -> unit
-val dp_timeout : int -> unit
-val dp_debug : bool -> unit
-val dp_trace : bool -> unit
-val dp_prelude : string list -> unit
-val dp_predefined : reference -> string -> unit
-
-
diff --git a/contrib/dp/dp_gappa.ml b/contrib/dp/dp_gappa.ml
deleted file mode 100644
index 9c035aa8..00000000
--- a/contrib/dp/dp_gappa.ml
+++ /dev/null
@@ -1,445 +0,0 @@
-
-open Format
-open Util
-open Pp
-open Term
-open Tacmach
-open Tactics
-open Tacticals
-open Names
-open Nameops
-open Termops
-open Coqlib
-open Hipattern
-open Libnames
-open Declarations
-open Evarutil
-
-let debug = ref false
-
-(* 1. gappa syntax trees and output *)
-
-module Constant = struct
-
-  open Bigint
-
-  type t = { mantissa : bigint; base : int; exp : bigint }
-
-  let create (b, m, e) =
-    { mantissa = m; base = b; exp = e }
-
-  let of_int x = 
-    { mantissa = x; base = 1; exp = zero }
-
-  let print fmt x = match x.base with
-    | 1 -> fprintf fmt "%s" (to_string x.mantissa)
-    | 2 -> fprintf fmt "%sb%s" (to_string x.mantissa) (to_string x.exp)
-    | 10 -> fprintf fmt "%se%s" (to_string x.mantissa) (to_string x.exp)
-    | _ -> assert false
-
-end
-
-type binop = Bminus | Bplus | Bmult | Bdiv
-
-type unop = Usqrt | Uabs | Uopp
-
-type rounding_mode = string
-
-type term =
-  | Tconst of Constant.t
-  | Tvar of string
-  | Tbinop of binop * term * term
-  | Tunop of unop * term
-  | Tround of rounding_mode * term
-
-type pred =
-  | Pin of term * Constant.t * Constant.t
-
-let rec print_term fmt = function
-  | Tconst c -> Constant.print fmt c
-  | Tvar s -> pp_print_string fmt s
-  | Tbinop (op, t1, t2) -> 
-      let op = match op with 
-	| Bplus -> "+" | Bminus -> "-" | Bmult -> "*" | Bdiv -> "/"
-      in
-      fprintf fmt "(%a %s %a)" print_term t1 op print_term t2
-  | Tunop (Uabs, t) ->
-      fprintf fmt "|%a|" print_term t
-  | Tunop (Uopp | Usqrt as op, t) ->
-      let s = match op with 
-	| Uopp -> "-" | Usqrt -> "sqrt" | _ -> assert false 
-      in
-      fprintf fmt "(%s(%a))" s print_term t
-  | Tround (m, t) ->
-      fprintf fmt "(%s(%a))" m print_term t
-
-let print_pred fmt = function
-  | Pin (t, c1, c2) -> 
-      fprintf fmt "%a in [%a, %a]" 
-	print_term t Constant.print c1 Constant.print c2
-
-let temp_file f = if !debug then f else Filename.temp_file f ".v"
-let remove_file f = if not !debug then try Sys.remove f with _ -> ()
-
-let read_gappa_proof f =
-  let buf = Buffer.create 1024 in
-  Buffer.add_char buf '(';
-  let cin = open_in f in
-  let rec skip_space () =
-    let c = input_char cin in if c = ' ' then skip_space () else c
-  in
-  while input_char cin <> '=' do () done;
-  try
-    while true do
-      let c = skip_space () in
-      if c = ':' then raise Exit;
-      Buffer.add_char buf c;
-      let s = input_line cin in
-      Buffer.add_string buf s; 
-      Buffer.add_char buf '\n';
-    done;
-    assert false
-  with Exit ->
-    close_in cin;
-    remove_file f;
-    Buffer.add_char buf ')';
-    Buffer.contents buf
-
-exception GappaFailed
-exception GappaProofFailed
-
-let patch_gappa_proof fin fout =
-  let cin = open_in fin in
-  let cout = open_out fout in
-  let fmt = formatter_of_out_channel cout in
-  let last = ref "" in
-  let defs = ref "" in
-  try
-    while true do
-      let s = input_line cin in
-      if s = "Qed." then
-	fprintf fmt "Defined.@\n"
-      else begin
-	begin 
-	  try Scanf.sscanf s "Lemma %s " 
-	    (fun n -> defs := n ^ " " ^ !defs; last := n)
-	  with Scanf.Scan_failure _ ->
-	    try Scanf.sscanf s "Definition %s " 
-	      (fun n -> defs := n ^ " " ^ !defs)
-	    with Scanf.Scan_failure _ ->
-	      ()
-	end;
-	fprintf fmt "%s@\n" s
-      end
-    done
-  with End_of_file ->
-    close_in cin;
-    fprintf fmt "Definition proof := Eval cbv delta [%s] in %s.@." !defs !last;
-    close_out cout
-    
-let call_gappa hl p =
-  let gappa_in = temp_file "gappa_input" in
-  let c = open_out gappa_in in
-  let fmt = formatter_of_out_channel c in
-  fprintf fmt "@[{ "; 
-  List.iter (fun h -> fprintf fmt "%a ->@ " print_pred h) hl;
-  fprintf fmt "%a }@]@." print_pred p;
-  close_out c;
-  let gappa_out = temp_file "gappa_output" in
-  let cmd = sprintf "gappa -Bcoq < %s > %s 2> /dev/null" gappa_in gappa_out in
-  let out = Sys.command cmd in
-  if out <> 0 then raise GappaFailed;
-  remove_file gappa_in;
-  let gappa_out2 = temp_file "gappa2" in
-  patch_gappa_proof gappa_out gappa_out2;
-  remove_file gappa_out;
-  let cmd = (Filename.concat (Envars.coqbin ()) "coqc") ^ " " ^ gappa_out2 in
-  let out = Sys.command cmd in
-  if out <> 0 then raise GappaProofFailed;
-  let gappa_out3 = temp_file "gappa3" in
-  let c = open_out gappa_out3 in
-  let gappa2 = Filename.chop_suffix (Filename.basename gappa_out2) ".v" in
-  Printf.fprintf c 
-    "Require \"%s\". Set Printing Depth 999999. Print %s.proof." 
-    (Filename.chop_suffix gappa_out2 ".v") gappa2;
-  close_out c;
-  let lambda = temp_file "gappa_lambda" in
-  let cmd = (Filename.concat (Envars.coqbin ()) "coqc") ^ " " ^ gappa_out3 ^ " > " ^ lambda in
-  let out = Sys.command cmd in
-  if out <> 0 then raise GappaProofFailed;
-  remove_file gappa_out2; remove_file gappa_out3;
-  remove_file (gappa_out2 ^ "o"); remove_file (gappa_out3 ^ "o");
-  read_gappa_proof lambda
-
-(* 2. coq -> gappa translation *)
-
-exception NotGappa
-
-let logic_dir = ["Coq";"Logic";"Decidable"]
-let coq_modules =
-  init_modules @ [logic_dir] @ arith_modules @ zarith_base_modules
-    @ [["Coq"; "ZArith"; "BinInt"];
-       ["Coq"; "Reals"; "Rdefinitions"]; 
-       ["Coq"; "Reals"; "Raxioms";];
-       ["Coq"; "Reals"; "Rbasic_fun";];
-       ["Coq"; "Reals"; "R_sqrt";];
-       ["Coq"; "Reals"; "Rfunctions";];
-       ["Gappa"; "Gappa_tactic";];
-       ["Gappa"; "Gappa_fixed";];
-       ["Gappa"; "Gappa_float";];
-       ["Gappa"; "Gappa_round_def";];
-       ["Gappa"; "Gappa_pred_bnd";];  
-       ["Gappa"; "Gappa_definitions";];
-  ]
-
-let constant = gen_constant_in_modules "gappa" coq_modules
-
-let coq_refl_equal = lazy (constant "refl_equal")
-let coq_Rle = lazy (constant "Rle")
-let coq_R = lazy (constant "R")
-(*
-let coq_Rplus = lazy (constant "Rplus")
-let coq_Rminus = lazy (constant "Rminus")
-let coq_Rmult = lazy (constant "Rmult")
-let coq_Rdiv = lazy (constant "Rdiv")
-let coq_powerRZ = lazy (constant "powerRZ")
-let coq_R1 = lazy (constant "R1")
-let coq_Ropp = lazy (constant "Ropp")
-let coq_Rabs = lazy (constant "Rabs")
-let coq_sqrt = lazy (constant "sqrt")
-*)
-
-let coq_convert = lazy (constant "convert")
-let coq_reUnknown = lazy (constant "reUnknown")
-let coq_reFloat2 = lazy (constant "reFloat2")
-let coq_reFloat10 = lazy (constant "reFloat10")
-let coq_reInteger = lazy (constant "reInteger")
-let coq_reBinary = lazy (constant "reBinary")
-let coq_reUnary = lazy (constant "reUnary")
-let coq_reRound = lazy (constant "reRound")
-let coq_roundDN = lazy (constant "roundDN")
-let coq_roundUP = lazy (constant "roundUP")
-let coq_roundNE = lazy (constant "roundNE")
-let coq_roundZR = lazy (constant "roundZR")
-let coq_rounding_fixed = lazy (constant "rounding_fixed")
-let coq_rounding_float = lazy (constant "rounding_float")
-let coq_boAdd = lazy (constant "boAdd")
-let coq_boSub = lazy (constant "boSub")
-let coq_boMul = lazy (constant "boMul")
-let coq_boDiv = lazy (constant "boDiv")
-let coq_uoAbs = lazy (constant "uoAbs")
-let coq_uoNeg = lazy (constant "uoNeg")
-let coq_uoSqrt = lazy (constant "uoSqrt")
-let coq_subset = lazy (constant "subset")
-let coq_makepairF = lazy (constant "makepairF")
-
-let coq_true = lazy (constant "true")
-let coq_false = lazy (constant "false")
-
-let coq_Z0 = lazy (constant "Z0")
-let coq_Zpos = lazy (constant "Zpos")
-let coq_Zneg = lazy (constant "Zneg")
-let coq_xH = lazy (constant "xH")
-let coq_xI = lazy (constant "xI")
-let coq_xO = lazy (constant "xO")
-let coq_IZR = lazy (constant "IZR")
-
-(* translates a closed Coq term p:positive into a FOL term of type int *)
-let rec tr_positive p = match kind_of_term p with
-  | Term.Construct _ when p = Lazy.force coq_xH ->
-      1
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xI ->
-      2 * (tr_positive a) + 1
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xO ->
-      2 * (tr_positive a)
-  | Term.Cast (p, _, _) ->
-      tr_positive p
-  | _ ->
-      raise NotGappa
-
-(* translates a closed Coq term t:Z into a term of type int *)
-let rec tr_arith_constant t = match kind_of_term t with
-  | Term.Construct _ when t = Lazy.force coq_Z0 -> 0
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zpos -> tr_positive a
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zneg -> - (tr_positive a)
-  | Term.Cast (t, _, _) -> tr_arith_constant t
-  | _ -> raise NotGappa
-
-(* translates a closed Coq term p:positive into a FOL term of type bigint *)
-let rec tr_bigpositive p = match kind_of_term p with
-  | Term.Construct _ when p = Lazy.force coq_xH -> 
-      Bigint.one
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xI ->
-      Bigint.add_1 (Bigint.mult_2 (tr_bigpositive a))
-  | Term.App (f, [|a|]) when f = Lazy.force coq_xO ->
-      (Bigint.mult_2 (tr_bigpositive a))
-  | Term.Cast (p, _, _) ->
-      tr_bigpositive p
-  | _ ->
-      raise NotGappa
-
-(* translates a closed Coq term t:Z into a term of type bigint *)
-let rec tr_arith_bigconstant t = match kind_of_term t with
-  | Term.Construct _ when t = Lazy.force coq_Z0 -> Bigint.zero
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zpos -> tr_bigpositive a
-  | Term.App (f, [|a|]) when f = Lazy.force coq_Zneg -> 
-      Bigint.neg (tr_bigpositive a)
-  | Term.Cast (t, _, _) -> tr_arith_bigconstant t
-  | _ -> raise NotGappa
-
-let decomp c = 
-  let c, args = decompose_app c in
-  kind_of_term c, args
-
-let tr_bool c = match decompose_app c with
-  | c, [] when c = Lazy.force coq_true -> true
-  | c, [] when c = Lazy.force coq_false -> false
-  | _ -> raise NotGappa
-
-let tr_float b m e =
-  (b, tr_arith_bigconstant m, tr_arith_bigconstant e)
-
-let tr_binop c = match decompose_app c with
-  | c, [] when c = Lazy.force coq_boAdd -> Bplus
-  | c, [] when c = Lazy.force coq_boSub -> Bminus
-  | c, [] when c = Lazy.force coq_boMul -> Bmult
-  | c, [] when c = Lazy.force coq_boDiv -> Bdiv
-  | _ -> assert false
-
-let tr_unop c = match decompose_app c with
-  | c, [] when c = Lazy.force coq_uoNeg -> Uopp
-  | c, [] when c = Lazy.force coq_uoSqrt -> Usqrt
-  | c, [] when c = Lazy.force coq_uoAbs -> Uabs
-  | _ -> raise NotGappa
-
-let tr_var c = match decomp c with
-  | Var x, [] -> string_of_id x
-  | _ -> assert false
-
-let tr_mode c = match decompose_app c with
-  | c, [] when c = Lazy.force coq_roundDN -> "dn"
-  | c, [] when c = Lazy.force coq_roundNE -> "ne"
-  | c, [] when c = Lazy.force coq_roundUP -> "up"
-  | c, [] when c = Lazy.force coq_roundZR -> "zr"
-  | _ -> raise NotGappa
-
-let tr_rounding_mode c = match decompose_app c with
-  | c, [a;b] when c = Lazy.force coq_rounding_fixed ->
-      let a = tr_mode a in
-      let b = tr_arith_constant b in
-      sprintf "fixed<%d,%s>" b a
-  | c, [a;p;e] when c = Lazy.force coq_rounding_float ->
-      let a = tr_mode a in
-      let p = tr_positive p in
-      let e = tr_arith_constant e in
-      sprintf "float<%d,%d,%s>" p (-e) a
-  | _ ->
-      raise NotGappa
-
-(* REexpr -> term *)
-let rec tr_term c0 = 
-  let c, args = decompose_app c0 in
-  match kind_of_term c, args with
-    | _, [a] when c = Lazy.force coq_reUnknown ->
-	Tvar (tr_var a)
-    | _, [a; b] when c = Lazy.force coq_reFloat2 ->
-	Tconst (Constant.create (tr_float 2 a b))
-    | _, [a; b] when c = Lazy.force coq_reFloat10 ->
-	Tconst (Constant.create (tr_float 10 a b))
-    | _, [a] when c = Lazy.force coq_reInteger ->
-	Tconst (Constant.create (1, tr_arith_bigconstant a, Bigint.zero))
-    | _, [op;a;b] when c = Lazy.force coq_reBinary ->
-	Tbinop (tr_binop op, tr_term a, tr_term b)
-    | _, [op;a] when c = Lazy.force coq_reUnary ->
-	Tunop (tr_unop op, tr_term a)
-    | _, [op;a] when c = Lazy.force coq_reRound ->
-	Tround (tr_rounding_mode op, tr_term a)
-    | _ -> 
-	msgnl (str "tr_term: " ++ Printer.pr_constr c0); 
-	assert false
-
-let tr_rle c = 
-  let c, args = decompose_app c in
-  match kind_of_term c, args with
-    | _, [a;b] when c = Lazy.force coq_Rle ->  
-	begin match decompose_app a, decompose_app b with
-	  | (ac, [at]), (bc, [bt]) 
-	    when ac = Lazy.force coq_convert && bc = Lazy.force coq_convert ->
-	      at, bt
-	  | _ ->
-	      raise NotGappa
-	end
-    | _ -> 
-	raise NotGappa
-
-let tr_pred c =
-  let c, args = decompose_app c in
-  match kind_of_term c, args with
-    | _, [a;b] when c = build_coq_and () ->
-	begin match tr_rle a, tr_rle b with
-	  | (c1, t1), (t2, c2) when t1 = t2 -> 
-	      begin match tr_term c1, tr_term c2 with
-		| Tconst c1, Tconst c2 ->
-		    Pin (tr_term t1, c1, c2)
-		| _ -> 
-		    raise NotGappa
-	      end
-	  | _ -> 
-	      raise NotGappa
-	end
-    | _ -> 
-	raise NotGappa
-
-let is_R c = match decompose_app c with
-  | c, [] when c = Lazy.force coq_R -> true
-  | _ -> false
-
-let tr_hyps =
-  List.fold_left 
-    (fun acc (_,h) -> try tr_pred h :: acc with NotGappa -> acc) []
-
-let constr_of_string gl s = 
-  let parse_constr = Pcoq.parse_string Pcoq.Constr.constr in
-  Constrintern.interp_constr (project gl) (pf_env gl) (parse_constr s)
-
-let var_name = function
-  | Name id -> 
-      let s = string_of_id id in
-      let s = String.sub s 1 (String.length s - 1) in
-      mkVar (id_of_string s)
-  | Anonymous -> 
-       assert false
-
-let build_proof_term c0 =
-  let bl,c = decompose_lam c0 in
-  List.fold_right 
-    (fun (x,t) pf -> 
-      mkApp (pf, [| if is_R t then var_name x else mk_new_meta () |]))
-    bl c0
-
-let gappa_internal gl =
-  try
-    let c = tr_pred (pf_concl gl) in
-    let s = call_gappa (tr_hyps (pf_hyps_types gl)) c in
-    let pf = constr_of_string gl s in
-    let pf = build_proof_term pf in
-    Tacticals.tclTHEN (Tacmach.refine_no_check pf) Tactics.assumption gl
-  with 
-    | NotGappa -> error "not a gappa goal"
-    | GappaFailed -> error "gappa failed"
-    | GappaProofFailed -> error "incorrect gappa proof term"
-
-let gappa_prepare =
-  let id = Ident (dummy_loc, id_of_string "gappa_prepare") in
-  lazy (Tacinterp.interp (Tacexpr.TacArg (Tacexpr.Reference id)))
-
-let gappa gl =
-  Coqlib.check_required_library ["Gappa"; "Gappa_tactic"];
-  Tacticals.tclTHEN (Lazy.force gappa_prepare) gappa_internal gl
-
-(*
-Local Variables: 
-compile-command: "make -C ../.. bin/coqc.opt bin/coqide.opt"
-End: 
-*)
-
diff --git a/contrib/dp/dp_why.ml b/contrib/dp/dp_why.ml
deleted file mode 100644
index e24049ad..00000000
--- a/contrib/dp/dp_why.ml
+++ /dev/null
@@ -1,151 +0,0 @@
-
-(* Pretty-print PFOL (see fol.mli) in Why syntax *)
-
-open Format
-open Fol
-
-type proof = 
-  | Immediate of Term.constr
-  | Fun_def of string * (string * typ) list * typ * term
-
-let proofs = Hashtbl.create 97
-let proof_name = 
-  let r = ref 0 in fun () -> incr r; "dp_axiom__" ^ string_of_int !r
-
-let add_proof pr = let n = proof_name () in Hashtbl.add proofs n pr; n
-
-let find_proof = Hashtbl.find proofs
-
-let rec print_list sep print fmt = function
-  | [] -> ()
-  | [x] -> print fmt x
-  | x :: r -> print fmt x; sep fmt (); print_list sep print fmt r
-
-let space fmt () = fprintf fmt "@ "
-let comma fmt () = fprintf fmt ",@ "
-
-let is_why_keyword = 
-  let h = Hashtbl.create 17 in
-  List.iter 
-    (fun s -> Hashtbl.add h s ())
-    ["absurd"; "and"; "array"; "as"; "assert"; "axiom"; "begin";
-     "bool"; "do"; "done"; "else"; "end"; "exception"; "exists";
-     "external"; "false"; "for"; "forall"; "fun"; "function"; "goal";
-     "if"; "in"; "int"; "invariant"; "label"; "let"; "logic"; "not";
-     "of"; "or"; "parameter"; "predicate"; "prop"; "raise"; "raises";
-     "reads"; "real"; "rec"; "ref"; "returns"; "then"; "true"; "try";
-     "type"; "unit"; "variant"; "void"; "while"; "with"; "writes" ]; 
-  Hashtbl.mem h
-
-let ident fmt s =
-  if is_why_keyword s then fprintf fmt "coq__%s" s else fprintf fmt "%s" s
-
-let rec print_typ fmt = function
-  | Tvar x -> fprintf fmt "'%a" ident x
-  | Tid ("int", []) -> fprintf fmt "int"
-  | Tid (x, []) -> fprintf fmt "%a" ident x
-  | Tid (x, [t]) -> fprintf fmt "%a %a" print_typ t ident x
-  | Tid (x,tl) -> fprintf fmt "(%a) %a" (print_list comma print_typ) tl ident x
-
-let rec print_term fmt = function
-  | Cst n -> 
-      fprintf fmt "%d" n
-  | Plus (a, b) ->
-      fprintf fmt "@[(%a +@ %a)@]" print_term a print_term b
-  | Moins (a, b) ->
-      fprintf fmt "@[(%a -@ %a)@]" print_term a print_term b
-  | Mult (a, b) ->
-      fprintf fmt "@[(%a *@ %a)@]" print_term a print_term b
-  | Div (a, b) ->
-      fprintf fmt "@[(%a /@ %a)@]" print_term a print_term b
-  | App (id, []) ->
-      fprintf fmt "%a" ident id
-  | App (id, tl) ->
-      fprintf fmt "@[%a(%a)@]" ident id print_terms tl
-
-and print_terms fmt tl = 
-  print_list comma print_term fmt tl
-
-let rec print_predicate fmt p = 
-  let pp = print_predicate in 
-  match p with
-  | True ->
-      fprintf fmt "true"
-  | False ->
-      fprintf fmt "false"
-  | Fatom (Eq (a, b)) ->
-      fprintf fmt "@[(%a =@ %a)@]" print_term a print_term b
-  | Fatom (Le (a, b)) ->
-      fprintf fmt "@[(%a <=@ %a)@]" print_term a print_term b
-  | Fatom (Lt (a, b))->
-      fprintf fmt "@[(%a <@ %a)@]" print_term a print_term b
-  | Fatom (Ge (a, b)) ->
-      fprintf fmt "@[(%a >=@ %a)@]" print_term a print_term b
-  | Fatom (Gt (a, b)) ->
-      fprintf fmt "@[(%a >@ %a)@]" print_term a print_term b
-  | Fatom (Pred (id, [])) -> 
-      fprintf fmt "%a" ident id
-  | Fatom (Pred (id, tl)) -> 
-      fprintf fmt "@[%a(%a)@]" ident id print_terms tl
-  | Imp (a, b) ->
-      fprintf fmt "@[(%a ->@ %a)@]" pp a pp b
-  | Iff (a, b) ->
-      fprintf fmt "@[(%a <->@ %a)@]" pp a pp b
-  | And (a, b) ->
-      fprintf fmt "@[(%a and@ %a)@]" pp a pp b
-  | Or (a, b) ->
-      fprintf fmt "@[(%a or@ %a)@]" pp a pp b
-  | Not a ->
-      fprintf fmt "@[(not@ %a)@]" pp a
-  | Forall (id, t, p) -> 
-      fprintf fmt "@[(forall %a:%a.@ %a)@]" ident id print_typ t pp p
-  | Exists (id, t, p) -> 
-      fprintf fmt "@[(exists %a:%a.@ %a)@]" ident id print_typ t pp p
-
-let print_query fmt (decls,concl) =
-  let print_dtype = function
-    | DeclType (id, 0) ->
-	fprintf fmt "@[type %a@]@\n@\n" ident id
-    | DeclType (id, 1) ->
-	fprintf fmt "@[type 'a %a@]@\n@\n" ident id
-    | DeclType (id, n) ->
-	fprintf fmt "@[type (";
-	for i = 1 to n do 
-	  fprintf fmt "'a%d" i; if i < n then fprintf fmt ", "
-	done;
-	fprintf fmt ") %a@]@\n@\n" ident id
-    | DeclFun _ | DeclPred _ | Axiom _ ->
-	()
-  in
-  let print_dvar_dpred = function
-    | DeclFun (id, _, [], t) ->
-	fprintf fmt "@[logic %a : -> %a@]@\n@\n" ident id print_typ t
-    | DeclFun (id, _, l, t) ->
-	fprintf fmt "@[logic %a : %a -> %a@]@\n@\n" 
-	  ident id (print_list comma print_typ) l print_typ t
-    | DeclPred (id, _, []) ->
-	fprintf fmt "@[logic %a : -> prop @]@\n@\n" ident id
-    | DeclPred (id, _, l) -> 
-	fprintf fmt "@[logic %a : %a -> prop@]@\n@\n" 
-	  ident id (print_list comma print_typ) l
-    | DeclType _ | Axiom _ ->
-	()
-  in
-  let print_assert = function
-    | Axiom (id, f)  -> 
-	fprintf fmt "@[<hov 2>axiom %a:@ %a@]@\n@\n" ident id print_predicate f
-    | DeclType _ | DeclFun _ | DeclPred _ ->
-	()
-  in
-  List.iter print_dtype decls;
-  List.iter print_dvar_dpred decls;
-  List.iter print_assert decls;
-  fprintf fmt "@[<hov 2>goal coq___goal: %a@]" print_predicate concl
-
-let output_file f q =
-  let c = open_out f in
-  let fmt = formatter_of_out_channel c in
-  fprintf fmt "@[%a@]@." print_query q;
-  close_out c
-
-
diff --git a/contrib/dp/dp_why.mli b/contrib/dp/dp_why.mli
deleted file mode 100644
index b38a3d37..00000000
--- a/contrib/dp/dp_why.mli
+++ /dev/null
@@ -1,17 +0,0 @@
-
-open Fol
-
-(* generation of the Why file *)
-
-val output_file : string -> query -> unit
-
-(* table to translate the proofs back to Coq (used in dp_zenon) *)
-
-type proof = 
-  | Immediate of Term.constr
-  | Fun_def of string * (string * typ) list * typ * term
-
-val add_proof : proof -> string
-val find_proof : string -> proof
-
-
diff --git a/contrib/dp/dp_zenon.mli b/contrib/dp/dp_zenon.mli
deleted file mode 100644
index 0a727d1f..00000000
--- a/contrib/dp/dp_zenon.mli
+++ /dev/null
@@ -1,7 +0,0 @@
-
-open Fol
-
-val set_debug : bool -> unit
-
-val proof_from_file : string -> Proof_type.tactic
-
diff --git a/contrib/dp/dp_zenon.mll b/contrib/dp/dp_zenon.mll
deleted file mode 100644
index e15e280d..00000000
--- a/contrib/dp/dp_zenon.mll
+++ /dev/null
@@ -1,181 +0,0 @@
-
-{
-
-  open Lexing 
-  open Pp
-  open Util
-  open Names
-  open Tacmach
-  open Dp_why
-  open Tactics
-  open Tacticals
-
-  let debug = ref false
-  let set_debug b = debug := b
-  
-  let buf = Buffer.create 1024
-    
-  let string_of_global env ref =
-    Libnames.string_of_qualid (Nametab.shortest_qualid_of_global env ref)
-
-  let axioms = ref []
-
-  (* we cannot interpret the terms as we read them (since some lemmas
-     may need other lemmas to be already interpreted) *)
-  type lemma = { l_id : string; l_type : string; l_proof : string }
-  type zenon_proof = lemma list * string
-
-}
-
-let ident = ['a'-'z' 'A'-'Z' '_' '0'-'9' '\'']+
-let space = [' ' '\t' '\r']
-
-rule start = parse
-| "(* BEGIN-PROOF *)" "\n" { scan lexbuf }
-| _ { start lexbuf }
-| eof { anomaly "malformed Zenon proof term" }
-
-(* here we read the lemmas and the main proof term;
-   meanwhile we maintain the set of axioms that were used *)
-
-and scan = parse
-| "Let" space (ident as id) space* ":"
-  { let t = read_coq_term lexbuf in
-    let p = read_lemma_proof lexbuf in
-    let l,pr = scan lexbuf in
-    { l_id = id; l_type = t; l_proof = p } :: l, pr }
-| "Definition theorem:"
-  { let t = read_main_proof lexbuf in [], t }
-| _ | eof
-  { anomaly "malformed Zenon proof term" }
-
-and read_coq_term = parse
-| "." "\n" 
-  { let s = Buffer.contents buf in Buffer.clear buf; s }
-| "coq__" (ident as id) (* a Why keyword renamed *)
-  { Buffer.add_string buf id; read_coq_term lexbuf }
-| ("dp_axiom__" ['0'-'9']+) as id 
-  { axioms := id :: !axioms; Buffer.add_string buf id; read_coq_term lexbuf }
-| _ as c 
-  { Buffer.add_char buf c; read_coq_term lexbuf }
-| eof 
-  { anomaly "malformed Zenon proof term" }
-
-and read_lemma_proof = parse
-| "Proof" space
-  { read_coq_term lexbuf }
-| _ | eof
-  { anomaly "malformed Zenon proof term" }
-
-(* skip the main proof statement and then read its term *)
-and read_main_proof = parse
-| ":=" "\n"
-  { read_coq_term lexbuf }
-| _ 
-  { read_main_proof lexbuf }
-| eof
-  { anomaly "malformed Zenon proof term" }
-
-
-{
-
-  let read_zenon_proof f =
-    Buffer.clear buf;
-    let c = open_in f in
-    let lb = from_channel c in
-    let p = start lb in
-    close_in c;
-    if not !debug then begin try Sys.remove f with _ -> () end;
-    p
-
-  let constr_of_string gl s = 
-    let parse_constr = Pcoq.parse_string Pcoq.Constr.constr in
-    Constrintern.interp_constr (project gl) (pf_env gl) (parse_constr s)
-
-  (* we are lazy here: we build strings containing Coq terms using a *)
-  (* pretty-printer Fol -> Coq *)
-  module Coq = struct
-    open Format
-    open Fol
-
-    let rec print_list sep print fmt = function
-      | [] -> ()
-      | [x] -> print fmt x
-      | x :: r -> print fmt x; sep fmt (); print_list sep print fmt r
-	  
-    let space fmt () = fprintf fmt "@ "
-    let comma fmt () = fprintf fmt ",@ "
-
-    let rec print_typ fmt = function
-      | Tvar x -> fprintf fmt "%s" x
-      | Tid ("int", []) -> fprintf fmt "Z"
-      | Tid (x, []) -> fprintf fmt "%s" x
-      | Tid (x, [t]) -> fprintf fmt "(%s %a)" x print_typ t 
-      | Tid (x,tl) -> 
-	  fprintf fmt "(%s %a)" x (print_list comma print_typ) tl 
-	  
-    let rec print_term fmt = function
-      | Cst n -> 
-	  fprintf fmt "%d" n
-      | Plus (a, b) ->
-	  fprintf fmt "@[(Zplus %a %a)@]" print_term a print_term b
-      | Moins (a, b) ->
-	  fprintf fmt "@[(Zminus %a %a)@]" print_term a print_term b
-      | Mult (a, b) ->
-	  fprintf fmt "@[(Zmult %a %a)@]" print_term a print_term b
-      | Div (a, b) ->
-	  fprintf fmt "@[(Zdiv %a %a)@]" print_term a print_term b
-      | App (id, []) ->
-	  fprintf fmt "%s" id
-      | App (id, tl) ->
-	  fprintf fmt "@[(%s %a)@]" id print_terms tl
-
-    and print_terms fmt tl = 
-      print_list space print_term fmt tl
-
-    (* builds the text for "forall vars, f vars = t" *)
-    let fun_def_axiom f vars t =
-      let binder fmt (x,t) = fprintf fmt "(%s: %a)" x print_typ t in
-      fprintf str_formatter
-	"@[(forall %a, %s %a = %a)@]@."
-	(print_list space binder) vars f 
-	(print_list space (fun fmt (x,_) -> pp_print_string fmt x)) vars
-	print_term t;
-      flush_str_formatter ()
-			   
-  end
-
-  let prove_axiom id = match Dp_why.find_proof id with
-    | Immediate t -> 
-	exact_check t
-    | Fun_def (f, vars, ty, t) -> 
-	tclTHENS
-	  (fun gl ->
-	     let s = Coq.fun_def_axiom f vars t in
-	     if !debug then Format.eprintf "axiom fun def = %s@." s;
-	     let c = constr_of_string gl s in
-	     assert_tac (Name (id_of_string id)) c gl)
-	  [tclTHEN intros reflexivity; tclIDTAC]
-
-  let exact_string s gl =
-    let c = constr_of_string gl s in
-    exact_check c gl
-
-  let interp_zenon_proof (ll,p) =
-    let interp_lemma l gl =
-      let ty = constr_of_string gl l.l_type in
-      tclTHENS
-	(assert_tac (Name (id_of_string l.l_id)) ty)
-	[exact_string l.l_proof; tclIDTAC]
-	gl
-    in
-    tclTHEN (tclMAP interp_lemma ll) (exact_string p)
-
-  let proof_from_file f =
-    axioms := [];
-    msgnl (str "proof_from_file " ++ str f);
-    let zp = read_zenon_proof f in
-    msgnl (str "proof term is " ++ str (snd zp));
-    tclTHEN (tclMAP prove_axiom !axioms) (interp_zenon_proof zp)
-
-}
diff --git a/contrib/dp/fol.mli b/contrib/dp/fol.mli
deleted file mode 100644
index b94bd3e3..00000000
--- a/contrib/dp/fol.mli
+++ /dev/null
@@ -1,55 +0,0 @@
-
-(* Polymorphic First-Order Logic (that is Why's input logic) *)
-
-type typ = 
-  | Tvar of string
-  | Tid of string * typ list
-
-type term =   
-  | Cst of int
-  | Plus of term * term
-  | Moins of term * term
-  | Mult of term * term
-  | Div of term * term
-  | App of string * term list
-
-and atom =   
-  | Eq of term * term
-  | Le of term * term
-  | Lt of term * term
-  | Ge of term * term
-  | Gt of term * term
-  | Pred of string * term list
-
-and form = 
-  | Fatom of atom
-  | Imp of form * form
-  | Iff of form * form
-  | And of form * form
-  | Or of form * form
-  | Not of form
-  | Forall of string * typ * form
-  | Exists of string * typ * form
-  | True
-  | False
-
-(* the integer indicates the number of type variables *)
-type decl =
-  | DeclType of string * int
-  | DeclFun of string * int * typ list * typ
-  | DeclPred of string * int * typ list
-  | Axiom of string * form
-
-type query = decl list * form
-
-
-(* prover result *)
-
-type prover_answer = 
-  | Valid of string option 
-  | Invalid
-  | DontKnow
-  | Timeout
-  | NoAnswer
-  | Failure of string
-
diff --git a/contrib/dp/g_dp.ml4 b/contrib/dp/g_dp.ml4
deleted file mode 100644
index 99bcf477..00000000
--- a/contrib/dp/g_dp.ml4
+++ /dev/null
@@ -1,79 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i camlp4deps: "parsing/grammar.cma" i*)
-
-(* $Id: g_dp.ml4 10924 2008-05-13 14:01:11Z filliatr $ *)
-
-open Dp
-
-TACTIC EXTEND Simplify
-  [ "simplify" ] -> [ simplify ]
-END
-
-TACTIC EXTEND Ergo
-  [ "ergo" ] -> [ ergo ]
-END
-
-TACTIC EXTEND Yices
-  [ "yices" ] -> [ yices ]
-END
-
-TACTIC EXTEND CVCLite
-  [ "cvcl" ] -> [ cvc_lite ]
-END
-
-TACTIC EXTEND Harvey
-  [ "harvey" ] -> [ harvey ]
-END
-
-TACTIC EXTEND Zenon
-  [ "zenon" ] -> [ zenon ]
-END
-
-TACTIC EXTEND Gwhy
-  [ "gwhy" ] -> [ gwhy ]
-END
-
-TACTIC EXTEND Gappa_internal
-  [ "gappa_internal" ] -> [ Dp_gappa.gappa_internal ]
-END
-
-TACTIC EXTEND Gappa
-  [ "gappa" ] -> [ Dp_gappa.gappa ]
-END
-
-(* should be part of basic tactics syntax *)
-TACTIC EXTEND admit
-  [ "admit"    ] -> [ Tactics.admit_as_an_axiom ]
-END
-
-VERNAC COMMAND EXTEND Dp_hint 
-  [ "Dp_hint" ne_global_list(l) ] -> [ dp_hint l ]
-END
-
-VERNAC COMMAND EXTEND Dp_timeout
-| [ "Dp_timeout" natural(n) ] -> [ dp_timeout n ]
-END
-
-VERNAC COMMAND EXTEND Dp_prelude
-| [ "Dp_prelude" string_list(l) ] -> [ dp_prelude l ]
-END
-
-VERNAC COMMAND EXTEND Dp_predefined
-| [ "Dp_predefined" global(g) "=>" string(s) ] -> [ dp_predefined g s ]
-END
-
-VERNAC COMMAND EXTEND Dp_debug
-| [ "Dp_debug" ] -> [ dp_debug true; Dp_zenon.set_debug true ]
-END
-
-VERNAC COMMAND EXTEND Dp_trace
-| [ "Dp_trace" ] -> [ dp_trace true ]
-END
-
diff --git a/contrib/dp/test2.v b/contrib/dp/test2.v
deleted file mode 100644
index 3e4c0f6d..00000000
--- a/contrib/dp/test2.v
+++ /dev/null
@@ -1,80 +0,0 @@
-Require Import ZArith.
-Require Import Classical.
-Require Import List.
-
-Open Scope list_scope.
-Open Scope Z_scope.
-
-Dp_debug.
-Dp_timeout 3.
-Require Export zenon.
-
-Definition neg (z:Z) : Z := match z with
-  | Z0 => Z0
-  | Zpos p => Zneg p
-  | Zneg p => Zpos p
-  end.
-
-Goal forall z, neg (neg z) = z.
-  Admitted.
-
-Open Scope nat_scope.
-Print plus.
-
-Goal forall x, x+0=x.
-  induction x; ergo.
-  (* simplify resoud le premier, pas le second *)
-  Admitted.
-
-Goal 1::2::3::nil = 1::2::(1+2)::nil.
-  zenon.
-  Admitted.
-
-Definition T := nat.
-Parameter fct : T -> nat.
-Goal fct O = O.
- Admitted.
-
-Fixpoint even (n:nat) : Prop :=
-  match n with 
-  O => True
-  | S O => False
-  | S (S p) => even p
-  end.
-
-Goal even 4%nat.
-  try zenon.
-  Admitted.
-
-Definition p (A B:Set) (a:A) (b:B) : list (A*B) := cons (a,b) nil.
-
-Definition head :=
-fun (A : Set) (l : list A) =>
-match l with
-| nil => None (A:=A)
-| x :: _ => Some x
-end.
-
-Goal forall x, head _ (p _ _ 1 2) = Some x -> fst x = 1.
-
-Admitted.
-
-(*
-BUG avec head prédéfini : manque eta-expansion sur A:Set
-
-Goal forall x, head _ (p _ _ 1 2) = Some x -> fst x = 1.
-
-Print value. 
-Print Some.
- 
-zenon.
-*)
-
-Inductive IN (A:Set) : A -> list A -> Prop :=
-  | IN1 : forall x l, IN A x (x::l)
-  | IN2: forall x l, IN A x l -> forall y, IN A x (y::l).
-Implicit Arguments IN [A].
-
-Goal forall x, forall (l:list nat), IN x l -> IN x (1%nat::l).
-  zenon.
-Print In.
diff --git a/contrib/dp/test_gappa.v b/contrib/dp/test_gappa.v
deleted file mode 100644
index eb65a59d..00000000
--- a/contrib/dp/test_gappa.v
+++ /dev/null
@@ -1,91 +0,0 @@
-Require Export Gappa_tactic.
-Require Export Reals.
-
-Open Scope Z_scope.
-Open Scope R_scope.
-
-Lemma test_base10 : 
-  forall x y:R,
-  0 <= x <= 4 -> 
-  0 <= x * (24 * powerRZ 10 (-1)) <= 10.
-Proof.
-  gappa.
-Qed.
-
-(*
-@rnd = float< ieee_32, zr >;
-a = rnd(a_); b = rnd(b_);
-{ a in [3.2,3.3] /\ b in [1.4,1.9] ->
-  rnd(a - b) - (a - b) in [0,0] }
-*)
-
-Definition rnd := gappa_rounding (rounding_float roundZR 43 (120)).
-
-Lemma test_float3 :
-  forall a_ b_ a b : R,
-  a = rnd a_ ->
-  b = rnd b_ ->
-  52 / 16 <= a <= 53 / 16 ->
-  22 / 16 <= b <= 30 / 16 ->
-  0 <= rnd (a - b) - (a - b) <= 0.
-Proof.
-  unfold rnd.
-  gappa.
-Qed.
-
-Lemma test_float2 :
-  forall x y:R,
-  0 <= x <= 1 ->
-  0 <= y <= 1 ->
-  0 <= gappa_rounding (rounding_float roundNE 53 (1074)) (x+y) <= 2. 
-Proof.
-  gappa.
-Qed.
-
-Lemma test_float1 :
-  forall x y:R,
-  0 <= gappa_rounding (rounding_fixed roundDN (0)) x -
-           gappa_rounding (rounding_fixed roundDN (0)) y <= 0 ->
-  Rabs (x - y) <= 1.
-Proof.
-  gappa.
-Qed.
-
-Lemma test1 : 
-  forall x y:R,
-  0 <= x <= 1 -> 
-  0 <= -y <= 1 ->  
-  0 <= x  * (-y) <= 1.
-Proof.
-  gappa.
-Qed.
-
-Lemma test2 : 
-  forall x y:R,
-  3/4 <= x <= 3 -> 
-  0 <= sqrt x <= 1775 * (powerRZ 2 (-10)).
-Proof.
-  gappa.
-Qed.
-
-Lemma test3 : 
-  forall x y z:R,
-  0 <= x - y <= 3 -> 
-  -2 <= y - z <= 4 ->
-  -2 <= x - z <= 7.
-Proof.
-  gappa.
-Qed.
-
-Lemma test4 : 
-  forall x1 x2 y1 y2 : R,
-  1 <= Rabs y1 <= 1000 ->
-  1 <= Rabs y2 <= 1000 ->
-  - powerRZ 2 (-53) <= (x1 - y1) / y1 <= powerRZ 2 (-53) ->
-  - powerRZ 2 (-53) <= (x2 - y2) / y2 <= powerRZ 2 (-53) ->
-  - powerRZ 2 (-51) <= (x1 * x2 - y1 * y2) / (y1 * y2) <= powerRZ 2 (-51).
-Proof.
-  gappa.
-Qed.
-
-
diff --git a/contrib/dp/tests.v b/contrib/dp/tests.v
deleted file mode 100644
index a6d4f2e1..00000000
--- a/contrib/dp/tests.v
+++ /dev/null
@@ -1,288 +0,0 @@
-
-Require Import ZArith.
-Require Import Classical.
-
-Dp_debug.
-Dp_timeout 3.
-
-(* module renamings *)
-
-Module M.
-  Parameter t : Set.
-End M.
-
-Lemma test_module_0 : forall x:M.t, x=x.
-ergo.
-Qed.
-
-Module N := M.
-
-Lemma test_module_renaming_0 : forall x:N.t, x=x.
-ergo.
-Qed.
-
-Dp_predefined M.t => "int".
-
-Lemma test_module_renaming_1 : forall x:N.t, x=x.
-ergo.
-Qed.
-
-(* Coq lists *)
-
-Require Export List.
-
-Lemma test_pol_0 : forall l:list nat, l=l.
-ergo.
-Qed.
-
-Parameter nlist: list nat -> Prop.
-
-Lemma poly_1 : forall l,  nlist l -> True.
-intros. 
-simplify.
-Qed.
-
-(* user lists *)
-
-Inductive list (A:Set) : Set :=
-| nil : list A
-| cons: forall a:A, list A -> list A.
-
-Fixpoint app (A:Set) (l m:list A) {struct l} : list A :=
-match l with
-| nil => m
-| cons a l1 => cons A a (app A l1 m)
-end.
-
-Lemma entail: (nil Z) = app Z (nil Z) (nil Z) -> True. 
-intros; ergo. 
-Qed.
-
-(* polymorphism *)
-Require Import List.
-
-Inductive mylist (A:Set) : Set :=
-  mynil : mylist A
-| mycons : forall a:A, mylist A -> mylist A.
-
-Parameter my_nlist: mylist nat -> Prop.
-
- Goal forall l,  my_nlist l -> True.
- intros.
- simplify. 
-Qed.
-
-(* First example with the 0 and the equality translated *)
-
-Goal 0 = 0.
-simplify.
-Qed.
-
-(* Examples in the Propositional Calculus
-   and theory of equality *)
-
-Parameter A C : Prop.
-
-Goal A -> A.
-simplify.
-Qed.
-
-
-Goal A -> (A \/ C).
-
-simplify.
-Qed.
-
-
-Parameter x y z : Z.
-
-Goal x = y -> y = z -> x = z.
-ergo.
-Qed.
-
-
-Goal ((((A -> C) -> A) -> A) -> C) -> C.
-
-ergo.
-Qed.
-
-(* Arithmetic *)
-Open Scope Z_scope.
-
-Goal 1 + 1 = 2.
-yices.
-Qed.
-
-
-Goal 2*x + 10 = 18 -> x = 4.
-
-simplify.
-Qed.
-
-
-(* Universal quantifier *)
-
-Goal (forall (x y : Z), x = y) -> 0=1.
-try zenon.
-ergo.
-Qed.
-
-Goal forall (x: nat), (x + 0 = x)%nat.
-
-induction x0; ergo.
-Qed.
-
-
-(* No decision procedure can solve this problem 
-  Goal forall (x a b : Z), a * x + b = 0 -> x = - b/a.
-*)
-
-
-(* Functions definitions *) 
-
-Definition fst (x y : Z) : Z := x.
-
-Goal forall (g : Z -> Z) (x y : Z), g (fst x y) = g x.
-
-simplify.
-Qed.
-
-
-(* Eta-expansion example *)
-
-Definition snd_of_3 (x y z : Z) : Z := y.
-
-Definition f : Z -> Z -> Z := snd_of_3 0.
-
-Goal forall (x y z z1 : Z), snd_of_3 x y z = f y z1.
-
-simplify.
-Qed.
-
-
-(* Inductive types definitions - call to incontrib/dp/jection function *)
-
-Inductive even : Z -> Prop :=
-| even_0 : even 0
-| even_plus2 : forall z : Z, even z -> even (z + 2).
-
-
-(* Simplify and Zenon can't prove this goal before the timeout
-   unlike CVC Lite *)
-
-Goal even 4.
-ergo.
-Qed.
-
-
-Definition skip_z (z : Z) (n : nat) := n.
-
-Definition skip_z1 := skip_z.
-
-Goal forall (z : Z) (n : nat), skip_z z n = skip_z1 z n.
-yices.
-Qed.
-
-
-(* Axioms definitions and dp_hint *)
-
-Parameter add : nat -> nat -> nat.
-Axiom add_0 : forall (n : nat), add 0%nat n = n.
-Axiom add_S : forall (n1 n2 : nat), add (S n1) n2 = S (add n1 n2).
-
-Dp_hint add_0.
-Dp_hint add_S.
-
-(* Simplify can't prove this goal before the timeout 
-   unlike zenon *)
-
-Goal forall n : nat, add n 0 = n.
-induction n ; yices.
-Qed.
-
-
-Definition pred (n : nat) : nat := match n with
-  | 0%nat => 0%nat
-  | S n' => n'
-end.
-
-Goal forall n : nat, n <> 0%nat -> pred (S n) <> 0%nat.
-yices.
-(*zenon.*)
-Qed.
-
-
-Fixpoint plus (n m : nat) {struct n} : nat :=
-  match n with
-  | 0%nat => m
-  | S n' => S (plus n' m)
-end.
-
-Goal forall n : nat, plus n 0%nat = n.
-
-induction n; ergo.
-Qed.
-
-
-(* Mutually recursive functions *)
-
-Fixpoint even_b (n : nat) : bool := match n with
-  | O => true
-  | S m => odd_b m
-end
-with odd_b (n : nat) : bool := match n with
-  | O => false
-  | S m => even_b m
-end.
-
-Goal even_b (S (S O)) = true.
-ergo.
-(*
-simplify.
-zenon.
-*)
-Qed.
-
-
-(* sorts issues *)
-
-Parameter foo : Set.         
-Parameter ff : nat -> foo -> foo -> nat.
-Parameter g : foo -> foo.
-Goal (forall x:foo, ff 0 x x = O) -> forall y, ff 0 (g y) (g y) = O.
-yices.
-(*zenon.*)
-Qed.
-
-
-
-(* abstractions *)
-
-Parameter poly_f : forall A:Set, A->A.
-
-Goal forall x:nat, poly_f nat x = poly_f nat x.
-ergo.
-(*zenon.*)
-Qed.
-
-
-
-(* Anonymous mutually recursive functions : no equations are produced
-
-Definition mrf :=
-  fix even2 (n : nat) : bool := match n with
-    | O => true
-    | S m => odd2 m
-  end
-  with odd2 (n : nat) : bool := match n with
-    | O => false
-    | S m => even2 m
-  end for even.
-
-   Thus this goal is unsolvable
-
-Goal mrf (S (S O)) = true.
-
-zenon.
-
-*)
diff --git a/contrib/dp/zenon.v b/contrib/dp/zenon.v
deleted file mode 100644
index 4ad00a11..00000000
--- a/contrib/dp/zenon.v
+++ /dev/null
@@ -1,94 +0,0 @@
-(*  Copyright 2004 INRIA  *)
-(*  $Id: zenon.v 10739 2008-04-01 14:45:20Z herbelin $  *)
-
-Require Export Classical.
-
-Lemma zenon_nottrue :
-  (~True -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_noteq : forall (T : Type) (t : T),
-  ((t <> t) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_and : forall P Q : Prop,
-  (P -> Q -> False) -> (P /\ Q -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_or : forall P Q : Prop,
-  (P -> False) -> (Q -> False) -> (P \/ Q -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_imply : forall P Q : Prop,
-  (~P -> False) -> (Q -> False) -> ((P -> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_equiv : forall P Q : Prop,
-  (~P -> ~Q -> False) -> (P -> Q -> False) -> ((P <-> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notand : forall P Q : Prop,
-  (~P -> False) -> (~Q -> False) -> (~(P /\ Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notor : forall P Q : Prop,
-  (~P -> ~Q -> False) -> (~(P \/ Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notimply : forall P Q : Prop,
-  (P -> ~Q -> False) -> (~(P -> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_notequiv : forall P Q : Prop,
-  (~P -> Q -> False) -> (P -> ~Q -> False) -> (~(P <-> Q) -> False).
-Proof. tauto. Qed.
-
-Lemma zenon_ex : forall (T : Type) (P : T -> Prop),
-  (forall z : T, ((P z) -> False)) -> ((exists x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_all : forall (T : Type) (P : T -> Prop) (t : T),
-  ((P t) -> False) -> ((forall x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_notex : forall (T : Type) (P : T -> Prop) (t : T),
-  (~(P t) -> False) -> (~(exists x : T, (P x)) -> False).
-Proof. firstorder. Qed.
-
-Lemma zenon_notall : forall (T : Type) (P : T -> Prop),
-  (forall z : T, (~(P z) -> False)) -> (~(forall x : T, (P x)) -> False).
-Proof. intros T P Ha Hb. apply Hb. intro. apply NNPP. exact (Ha x). Qed.
-
-Lemma zenon_equal_base : forall (T : Type) (f : T), f = f.
-Proof. auto. Qed.
-
-Lemma zenon_equal_step :
-  forall (S T : Type) (fa fb : S -> T) (a b : S),
-  (fa = fb) -> (a <> b -> False) -> ((fa a) = (fb b)).
-Proof. intros. rewrite (NNPP (a = b)). congruence. auto. Qed.
-
-Lemma zenon_pnotp : forall P Q : Prop,
-  (P = Q) -> (P -> ~Q -> False).
-Proof. intros P Q Ha. rewrite Ha. auto. Qed.
-
-Lemma zenon_notequal : forall (T : Type) (a b : T),
-  (a = b) -> (a <> b -> False).
-Proof. auto. Qed.
-
-Ltac zenon_intro id :=
-  intro id || let nid := fresh in (intro nid; clear nid)
-.
-
-Definition zenon_and_s := fun P Q a b => zenon_and P Q b a.
-Definition zenon_or_s := fun P Q a b c => zenon_or P Q b c a.
-Definition zenon_imply_s := fun P Q a b c => zenon_imply P Q b c a.
-Definition zenon_equiv_s := fun P Q a b c => zenon_equiv P Q b c a.
-Definition zenon_notand_s := fun P Q a b c => zenon_notand P Q b c a.
-Definition zenon_notor_s := fun P Q a b => zenon_notor P Q b a.
-Definition zenon_notimply_s := fun P Q a b => zenon_notimply P Q b a.
-Definition zenon_notequiv_s := fun P Q a b c => zenon_notequiv P Q b c a.
-Definition zenon_ex_s := fun T P a b => zenon_ex T P b a.
-Definition zenon_notall_s := fun T P a b => zenon_notall T P b a.
-
-Definition zenon_pnotp_s := fun P Q a b c => zenon_pnotp P Q c a b.
-Definition zenon_notequal_s := fun T a b x y => zenon_notequal T a b y x.