- new devel contribs/LAMBDA-TYPES/Base-2 with the automatically generated

  procedural representation of the proofs in contribs/LAMBDA-TYPES/Base-1
- template_makefile_devel.in: %.mo.opt now works
- acic_procedural: some improvements
- PrimitiveTactics: a part of the elim tactic was factorixed for use by the
  procedural reconstruction

diff --git a/helm/software/components/acic_procedural/acic2Procedural.ml b/helm/software/components/acic_procedural/acic2Procedural.ml
index 3ee088696db48a6bc58eb67372214132f5df906c..9815580b6444ef8bb31669e0fd60aaae5cebb60b 100644 (file)
--- a/helm/software/components/acic_procedural/acic2Procedural.ml
+++ b/helm/software/components/acic_procedural/acic2Procedural.ml
@@ -191,26 +191,38 @@ let mk_exp_args hd tl classes synth =
    let args = aux args in
    if args = [] then hd else C.AAppl ("", hd :: args)
 
+let mk_convert st ?name sty ety note =
+   let e = Cn.hole "" in
+   let csty, cety = H.cic sty, H.cic ety in
+   let _note = Printf.sprintf "%s\nSINTH: %s\nEXP: %s"
+      note (Pp.ppterm csty) (Pp.ppterm cety)
+   in
+   if Ut.alpha_equivalence csty cety then [(* T.Note note *)] else 
+   match name with
+      | None         -> [T.Change (sty, ety, None, e, ""(*note*))]
+      | Some (id, i) -> 
+         begin match get_entry st id with
+           | C.Def _  -> assert false (* [T.ClearBody (id, note)] *)
+           | C.Decl _ -> [T.Change (ety, sty, Some (id, Some id), e, "" (* note *))] 
+         end
+
 let convert st ?name v = 
    match get_inner_types st v with
-      | None            -> []
-      | Some (sty, ety) ->
-        let e = Cn.hole "" in
-         let csty, cety = H.cic sty, H.cic ety in
-        if Ut.alpha_equivalence csty cety then [] else 
-        match name with
-           | None         -> [T.Change (sty, ety, None, e, "")]
-           | Some (id, i) -> 
-               begin match get_entry st id with
-                 | C.Def _  -> [T.ClearBody (id, "")]
-                 | C.Decl w -> 
-                    let w = S.lift i w in
-                    if Ut.alpha_equivalence csty w then [] 
-                    else 
-                    [T.Note (Pp.ppterm csty); T.Note (Pp.ppterm w);
-                    T.Change (sty, ety, Some (id, Some id), e, "")] 
-              end
-
+      | None            -> [(*T.Note "NORMAL: NO INNER TYPES"*)]
+      | Some (sty, ety) -> mk_convert st ?name sty ety "NORMAL"
+
+let convert_elim st ?name t v pattern =
+   match t, get_inner_types st t, get_inner_types st v with
+      | _, None, _
+      | _, _, None                                            -> [(* T.Note "ELIM: NO INNER TYPES"*)]
+      | C.AAppl (_, hd :: tl), Some (tsty, _), Some (vsty, _) ->
+         let where = List.hd (List.rev tl) in
+         let cty = Cn.elim_inferred_type 
+            st.context (H.cic vsty) (H.cic where) (H.cic hd) (H.cic pattern)
+        in
+         mk_convert st ?name (Cn.fake_annotate "" st.context cty) tsty "ELIM"
+      | _, Some _, Some _                                     -> assert false
+         
 let get_intro = function 
    | C.Anonymous -> None
    | C.Name s    -> Some s
@@ -230,23 +242,25 @@ let mk_arg st = function
    | C.ARel (_, _, i, name) as what -> convert st ~name:(name, i) what
    | _                              -> []
 
-let mk_fwd_rewrite st dtext name tl direction =   
+let mk_fwd_rewrite st dtext name tl direction t =   
    assert (List.length tl = 6);
    let what, where, predicate = List.nth tl 5, List.nth tl 3, List.nth tl 2 in
    let e = Cn.mk_pattern 1 predicate in
    match where with
-      | C.ARel (_, _, _, premise) ->
-         let script = mk_arg st what in
+      | C.ARel (_, _, i, premise) as v ->
          let where = Some (premise, name) in
+         let _script = convert_elim st ~name:(premise, i) t v e in 
+         let script = mk_arg st what @ mk_arg st v (* @ script *) in
         let st = {st with context = Cn.clear st.context premise} in 
         st, T.Rewrite (direction, what, where, e, dtext) :: script
       | _                         -> assert false
 
-let mk_rewrite st dtext what qs tl direction = 
+let mk_rewrite st dtext where qs tl direction t = 
    assert (List.length tl = 5);
    let predicate = List.nth tl 2 in
    let e = Cn.mk_pattern 1 predicate in
-   [T.Rewrite (direction, what, None, e, dtext); T.Branch (qs, "")]
+   let script = convert_elim st t t e in
+   script @ [T.Rewrite (direction, where, None, e, dtext); T.Branch (qs, "")]
 
 let rec proc_lambda st name v t =
    let dno = DTI.does_not_occur 1 (H.cic t) in
@@ -272,9 +286,9 @@ and proc_letin st what name v t =
          | Some (ity, _) ->
            let st, rqv = match v with
                | C.AAppl (_, hd :: tl) when is_fwd_rewrite_right hd tl ->
-                 mk_fwd_rewrite st dtext intro tl true
+                 mk_fwd_rewrite st dtext intro tl true v
               | C.AAppl (_, hd :: tl) when is_fwd_rewrite_left hd tl  ->
-                 mk_fwd_rewrite st dtext intro tl false
+                 mk_fwd_rewrite st dtext intro tl false v
               | v                                                     ->
                  let qs = [proc_proof (next st) v; [T.Id ""]] in
                  st, [T.Branch (qs, ""); T.Cut (intro, ity, dtext)]
@@ -300,7 +314,7 @@ and proc_rel st what =
 and proc_mutconstruct st what = 
    let _, dtext = test_depth st in
    let script = [T.Apply (what, dtext)] in 
-   mk_intros st what script   
+   mk_intros st what script
 
 and proc_appl st what hd tl =
    let proceed, dtext = test_depth st in
@@ -329,14 +343,14 @@ and proc_appl st what hd tl =
            let names = get_ind_names uri tyno in
            let qs = proc_bkd_proofs (next st) synth names classes tl in
             if is_rewrite_right hd then 
-              script @ mk_rewrite st dtext where qs tl false
+              script @ mk_rewrite st dtext where qs tl false what
            else if is_rewrite_left hd then 
-              script @ mk_rewrite st dtext where qs tl true
+              script @ mk_rewrite st dtext where qs tl true what
            else
               let predicate = List.nth tl (parsno - i) in
                let e = Cn.mk_pattern j predicate in
               let using = Some hd in
-              script @
+              convert_elim st what what e @ script @ 
               [T.Elim (where, using, e, dtext ^ text); T.Branch (qs, "")]
         | None        ->
            let qs = proc_bkd_proofs (next st) synth [] classes tl in

diff --git a/helm/software/components/acic_procedural/proceduralConversion.ml b/helm/software/components/acic_procedural/proceduralConversion.ml
index b8cdc08ea1b3af2a0288ef6239f3718ad4aed5ea..376313ac8f9de4577fbeae6780e57b33b6b77801 100644 (file)
--- a/helm/software/components/acic_procedural/proceduralConversion.ml
+++ b/helm/software/components/acic_procedural/proceduralConversion.ml
@@ -30,6 +30,8 @@ module TC   = CicTypeChecker
 module D    = Deannotate
 module UM   = UriManager
 module Rd   = CicReduction
+module PEH  = ProofEngineHelpers
+module PT   = PrimitiveTactics
 
 module DTI  = DoubleTypeInference
 
@@ -76,6 +78,46 @@ let lift k n =
    in
    lift_term k
 
+   let fake_annotate id c =
+      let get_binder c m =
+         try match List.nth c (pred m) with
+            | Some (C.Name s, _) -> s
+            | _ -> assert false
+         with
+            | Invalid_argument _ -> assert false
+      in
+      let mk_decl n v = Some (n, C.Decl v) in
+      let mk_def n v = Some (n, C.Def (v, None)) in
+      let mk_fix (name, _, _, bo) = mk_def (C.Name name) bo in
+      let mk_cofix (name, _, bo) = mk_def (C.Name name) bo in
+      let rec ann_xns c (uri, t) = uri, ann_term c t
+      and ann_ms c = function
+         | None -> None
+         | Some t -> Some (ann_term c t)
+      and ann_fix newc c (name, i, ty, bo) =
+         id, name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
+      and ann_cofix newc c (name, ty, bo) =
+         id, name, ann_term c ty, ann_term (List.rev_append newc c) bo
+      and ann_term c = function
+         | C.Sort sort -> C.ASort (id, sort)
+         | C.Implicit ann -> C.AImplicit (id, ann)
+         | C.Rel m -> C.ARel (id, id, m, get_binder c m)
+         | C.Const (uri, xnss) -> C.AConst (id, uri, List.map (ann_xns c) xnss)
+         | C.Var (uri, xnss) -> C.AVar (id, uri, List.map (ann_xns c) xnss)
+         | C.MutInd (uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (ann_xns c) xnss)
+         | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (ann_xns c) xnss)
+         | C.Meta (i, mss) -> C.AMeta(id, i, List.map (ann_ms c) mss)
+         | C.Appl ts -> C.AAppl (id, List.map (ann_term c) ts)
+         | C.Cast (te, ty) -> C.ACast (id, ann_term c te, ann_term c ty)
+         | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)
+         | C.Prod (n, s, t) -> C.AProd (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
+         | C.Lambda (n, s, t) -> C.ALambda (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
+         | C.LetIn (n, s, t) -> C.ALetIn (id, n, ann_term c s, ann_term (mk_def n s :: c) t)
+         | C.Fix (i, fl) -> C.AFix (id, i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
+         | C.CoFix (i, fl) -> C.ACoFix (id, i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
+      in
+      ann_term c
+
 let clear_absts m =
    let rec aux k n = function
       | C.AImplicit (_, None) as t         -> t
@@ -196,3 +238,14 @@ let clear c hyp =
       | entry :: tail -> aux (entry :: c) tail
    in
    aux [] c
+
+let elim_inferred_type context goal arg using cpattern =
+   let metasenv, ugraph = [], Un.empty_ugraph in 
+   let ety, _ugraph = TC.type_of_aux' metasenv context using ugraph in
+   let _splits, args_no = PEH.split_with_whd (context, ety) in
+   let _metasenv, predicate, _arg, actual_args = PT.mk_predicate_for_elim 
+      ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no
+   in
+   let ty = C.Appl (predicate :: actual_args) in
+   let upto = List.length actual_args in
+   Rd.head_beta_reduce ~delta:false ~upto ty

diff --git a/helm/software/components/acic_procedural/proceduralConversion.mli b/helm/software/components/acic_procedural/proceduralConversion.mli
index e5b2dcdcf9859e7f0ad2f23473053cce786fb205..ffc55d45e646bfbe7f26eabd251baf9b99830801 100644 (file)
--- a/helm/software/components/acic_procedural/proceduralConversion.mli
+++ b/helm/software/components/acic_procedural/proceduralConversion.mli
@@ -29,6 +29,8 @@ val hole: Cic.id -> Cic.annterm
 
 val lift: int -> int -> Cic.annterm -> Cic.annterm
 
+val fake_annotate: Cic.id -> Cic.context -> Cic.term -> Cic.annterm
+
 val mk_pattern: int -> Cic.annterm -> Cic.annterm
 
 val get_clears: 
@@ -36,3 +38,6 @@ val get_clears:
    Cic.context * string list
 
 val clear: Cic.context -> string -> Cic.context
+
+val elim_inferred_type:
+   Cic.context -> Cic.term -> Cic.term -> Cic.term -> Cic.term -> Cic.term

diff --git a/helm/software/components/tactics/primitiveTactics.ml b/helm/software/components/tactics/primitiveTactics.ml
index aeb0c0751286285b637a1cff94aae6854ee3cae4..e17d6cb7b68f16c5f4bac08b75fe91d3bdda4506 100644 (file)
--- a/helm/software/components/tactics/primitiveTactics.ml
+++ b/helm/software/components/tactics/primitiveTactics.ml
@@ -494,6 +494,58 @@ module S   = CicSubstitution
 module T   = Tacticals
 module RT  = ReductionTactics
 
+let rec args_init n f =
+   if n <= 0 then [] else f n :: args_init (pred n) f
+
+let mk_predicate_for_elim 
+ ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no = 
+   let instantiated_eliminator =
+      let f n = if n = 1 then arg else C.Implicit None in
+      C.Appl (using :: args_init args_no f)
+   in
+   let _actual_arg, iety, _metasenv', _ugraph = 
+      CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
+   in
+   let _actual_meta, actual_args = match iety with
+      | C.Meta (i, _)                  -> i, []
+      | C.Appl (C.Meta (i, _) :: args) -> i, args
+      | _                              -> assert false
+   in
+(* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
+   let rec mk_pred metasenv context' pred arg' = function
+      | []           -> metasenv, pred, arg'
+      | arg :: tail -> 
+(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
+         let argty, _ugraph = TC.type_of_aux' metasenv context' arg ugraph in
+         let argty = CicReduction.whd context' argty in         
+              let fresh_name = 
+            FreshNamesGenerator.mk_fresh_name 
+            ~subst:[] metasenv context' C.Anonymous ~typ:argty
+         in
+        let hyp = Some (fresh_name, C.Decl argty) in
+         let lazy_term c m u =  
+            let distance  = List.length c - List.length context in
+            S.lift distance arg, m, u
+         in
+         let pattern = Some lazy_term, [], Some cpattern in
+         let subst, metasenv, _ugraph, _conjecture, selected_terms =
+            ProofEngineHelpers.select
+            ~metasenv ~ugraph ~conjecture:(0, context, pred) ~pattern
+         in
+         let metasenv = MS.apply_subst_metasenv subst metasenv in  
+         let map (_context_of_t, t) l = t :: l in
+         let what = List.fold_right map selected_terms [] in
+         let arg' = MS.apply_subst subst arg' in
+         let argty = MS.apply_subst subst argty in
+         let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
+         let pred = MS.apply_subst subst pred in
+         let pred = C.Lambda (fresh_name, argty, pred) in
+         mk_pred metasenv (hyp :: context') pred arg' tail 
+   in
+   let metasenv, pred, arg = mk_pred metasenv context goal arg actual_args in
+   HLog.debug ("PRED: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
+   metasenv, pred, arg, actual_args
+
 let beta_after_elim_tac upto predicate =
    let beta_after_elim_tac status =
       let proof, goal = status in
@@ -559,9 +611,9 @@ let beta_after_elim_tac upto predicate =
    
 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term = 
  let elim_tac (proof, goal) =
-   let cpatt = match pattern with 
-      | None, [], Some cpatt -> cpatt
-      | _                    -> raise (PET.Fail (lazy "not implemented"))
+   let cpattern = match pattern with 
+      | None, [], Some cpattern -> cpattern
+      | _                       -> raise (PET.Fail (lazy "not implemented"))
    in    
    let ugraph = CicUniv.empty_ugraph in
    let curi, metasenv, _subst, proofbo, proofty, attrs = proof in
@@ -610,67 +662,20 @@ let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
          TC.type_of_aux' metasenv' context eliminator_ref ugraph in
 (* FG: ADDED PART ***********************************************************)
 (* FG: we can not assume eliminator is the default eliminator ***************)
-   let rec args_init n f =
-      if n <= 0 then [] else f n :: args_init (pred n) f
-   in
    let splits, args_no = PEH.split_with_whd (context, ety) in
    let pred_pos = match List.hd splits with
       | _, C.Rel i when i > 1 && i <= args_no -> i
       | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
       | _ -> raise NotAnEliminator
    in
-   let upto, metasenv', pred, term = match pattern with 
+   let metasenv', pred, term, actual_args = match pattern with 
       | None, [], Some (C.Implicit (Some `Hole)) ->
-         0, metasenv', C.Implicit None, term
+         metasenv', C.Implicit None, term, []
       | _                                        ->
-         let instantiated_eliminator =
-            let f n = if n = 1 then term else C.Implicit None in
-            C.Appl (eliminator_ref :: args_init args_no f)
-         in
-         let _actual_term, iety, _metasenv'', _ugraph = 
-            CicRefine.type_of_aux' metasenv' context instantiated_eliminator ugraph
-         in
-         let _actual_meta, actual_args = match iety with
-            | C.Meta (i, _)                  -> i, []
-            | C.Appl (C.Meta (i, _) :: args) -> i, args
-            | _                              -> assert false
-         in
-         (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
-         let upto = List.length actual_args in
-         let rec mk_pred metasenv context' pred term' = function
-            | []           -> metasenv, pred, term'
-            | term :: tail -> 
-(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
-               let termty, _ugraph = TC.type_of_aux' metasenv context' term ugraph in
-               let termty = CicReduction.whd context' termty in         
-              let fresh_name = 
-                  FreshNamesGenerator.mk_fresh_name 
-                  ~subst:[] metasenv context' C.Anonymous ~typ:termty
-               in
-              let hyp = Some (fresh_name, C.Decl termty) in
-               let lazy_term c m u =  
-                  let distance  = List.length c - List.length context in
-                  S.lift distance term, m, u
-               in
-               let pattern = Some lazy_term, [], Some cpatt in
-               let subst, metasenv, _ugraph, _conjecture, selected_terms =
-                  ProofEngineHelpers.select
-                  ~metasenv ~ugraph ~conjecture:(metano, context, pred) ~pattern
-               in
-               let metasenv = MS.apply_subst_metasenv subst metasenv in  
-               let map (_context_of_t, t) l = t :: l in
-               let what = List.fold_right map selected_terms [] in
-               let term' = MS.apply_subst subst term' in
-               let termty = MS.apply_subst subst termty in
-               let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
-               let pred = MS.apply_subst subst pred in
-               let pred = C.Lambda (fresh_name, termty, pred) in
-               mk_pred metasenv (hyp :: context') pred term' tail 
-         in
-         let metasenv', pred, term = mk_pred metasenv' context ty term actual_args in
-         HLog.debug ("PRED: " ^ CicPp.ppterm ~metasenv:metasenv' pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv:metasenv') actual_args));
-         upto, metasenv', pred, term
-      in
+         mk_predicate_for_elim 
+           ~args_no ~context ~ugraph ~cpattern
+           ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
+   in
 (* FG: END OF ADDED PART ****************************************************)
       let term_to_refine =
          let f n =
@@ -698,6 +703,7 @@ let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
            new_goals @ new_goals'
       in
       let res = proof'', patched_new_goals in
+      let upto = List.length actual_args in
       if upto = 0 then res else 
       let continuation = beta_after_elim_tac upto pred in
       let dummy_status = proof,goal in

diff --git a/helm/software/components/tactics/primitiveTactics.mli b/helm/software/components/tactics/primitiveTactics.mli
index 577ed753575a0da5dd6ecfd78b3cbdcb3e08481c..890874a89447507173fb3cfb19e27c286b646cb1 100644 (file)
--- a/helm/software/components/tactics/primitiveTactics.mli
+++ b/helm/software/components/tactics/primitiveTactics.mli
@@ -91,3 +91,9 @@ val cases_intros_tac:
 (* inserts a hole in the context *)
 val letout_tac:
   ProofEngineTypes.tactic 
+
+val mk_predicate_for_elim: 
+ context:Cic.context -> metasenv:Cic.metasenv -> 
+ ugraph:CicUniv.universe_graph -> goal:Cic.term -> 
+ arg:Cic.term -> using:Cic.term -> cpattern:Cic.term -> args_no:int -> 
+ Cic.metasenv * Cic.term * Cic.term * Cic.term list

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/Makefile b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/Makefile
new file mode 100644 (file)
index 0000000..2524510
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/Makefile
@@ -0,0 +1,27 @@
+include ../../../../Makefile.defs
+
+H=@
+
+MATITAC = $(RT_BASE_DIR)/matitac.opt
+
+MMAS = $(shell find -name "*.mma")
+MAS = $(MMAS:%.mma=%.ma)
+
+all: OPTIONS = -bench
+
+log: OPTIONS = >> tmp.txt 2>&1 
+ 
+all: $(MAS)
+
+log: $(MAS)
+       $(H)mv tmp.txt log.txt
+
+clean:
+       $(H)rm -f $(MAS)
+
+%.ma: %.mma
+       $(H)$(MATITAC) -dump $@ $< $(OPTIONS)  
+
+include depend
+
+.DELETE_ON_ERROR:

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/defs.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/defs.mma
new file mode 100644 (file)
index 0000000..34839d8
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/defs.mma
@@ -0,0 +1,23 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/blt/defs".
+
+include "preamble.ma".
+
+(* object blt not inlined *)
+
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/props.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/props.mma
new file mode 100644 (file)
index 0000000..d244663
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/blt/props.mma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/blt/props".
+
+include "blt/defs.ma".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/blt/props/lt_blt.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/blt/props/le_bge.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/blt/props/blt_lt.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/blt/props/bge_le.con".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/depend b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/depend
new file mode 100644 (file)
index 0000000..1f10a00
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/depend
@@ -0,0 +1,9 @@
+theory.ma: theory.mma ext/tactics.ma ext/arith.ma types/props.ma blt/props.ma plist/props.ma
+ext/tactics.ma: ext/tactics.mma preamble.ma
+ext/arith.ma: ext/arith.mma preamble.ma
+types/defs.ma: types/defs.mma preamble.ma
+types/props.ma: types/props.mma types/defs.ma
+blt/defs.ma: blt/defs.mma preamble.ma
+blt/props.ma: blt/props.mma blt/defs.ma
+plist/defs.ma: plist/defs.mma preamble.ma
+plist/props.ma: plist/props.mma plist/defs.ma

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/arith.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/arith.mma
new file mode 100644 (file)
index 0000000..240f138
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/arith.mma
@@ -0,0 +1,106 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/ext/arith".
+
+include "preamble.ma".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/nat_dec.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/simpl_plus_r.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_plus_r.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/plus_permute_2_in_3.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/plus_permute_2_in_3_assoc.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/plus_O.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_Sx_SO.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/eq_nat_dec.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/neq_eq_e.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_false.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_Sx_x.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_le.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_plus_minus_sym.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_minus_minus.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_minus_plus.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_minus.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_trans_plus_r.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_gen_S.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_x_plus_x_Sy.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/simpl_lt_plus_r.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_x_Sy.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_plus_minus.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_plus_minus_r.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_x_SO.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_x_pred_y.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_le_minus.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_le_e.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_eq_e.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_eq_gt_e.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_gen_xS.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_lt_false.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/lt_neq.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/arith0.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/O_minus.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/minus_minus.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/plus_plus.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/arith/le_S_minus.con".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/tactics.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/tactics.mma
new file mode 100644 (file)
index 0000000..18de7f7
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/ext/tactics.mma
@@ -0,0 +1,27 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/ext/tactics".
+
+include "preamble.ma".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/tactics/insert_eq.con".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/ext/tactics/unintro.con".
+
+inline procedural 
+"cic:/matita/LAMBDA-TYPES/Base-1/ext/tactics/xinduction.con".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/log.txt b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/log.txt
new file mode 100644 (file)
index 0000000..2c20deb
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/log.txt
@@ -0,0 +1,744 @@
+\e[0;32mInfo:  \e[0mexecution of blt/defs.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/blt ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./blt/defs.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of blt/defs.mma completed in 1''.
+\e[0;32mInfo:  \e[0mexecution of blt/props.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/blt ...''
+\e[0;32mInfo:  \e[0mbaseuri cic:/matita/LAMBDA-TYPES/Base-2/blt/props is not empty
+\e[0;32mInfo:  \e[0mcleaning baseuri cic:/matita/LAMBDA-TYPES/Base-2/blt/props
+\e[0;32mInfo:  \e[0mRemoving: cic:/matita/LAMBDA-TYPES/Base-2/blt/props/*
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./blt/defs.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/blt/defs" ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_blt
+Pre Nodes : 257
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((lt y n)\to (eq bool (blt y n) true)))) (\lambda y:nat.(\lambda H:(lt y O). let H0 \def (le_ind (S y) (\lambda n:nat.((eq nat n O)\to (eq bool (blt y O) true))) (\lambda H0:(eq nat (S y) O). let H1 \def (eq_ind nat (S y) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H0) in (False_ind (eq bool (blt y O) true) H1)) (\lambda m:nat.(\lambda H0:(le (S y) m).(\lambda _:((eq nat m O)\to (eq bool (blt y O) true)).(\lambda H1:(eq nat (S m) O). let H2 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in  let DEFINED \def (False_ind ((le (S y) m)\to (eq bool (blt y O) true)) H2) in (DEFINED H0))))) O H) in (H0 (refl_equal nat O)))) (\lambda n:nat.(\lambda H:(\forall y:nat.((lt y n)\to (eq bool (blt y n) true))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((lt n0 (S n))\to (eq bool (blt n0 (S n)) true))) (\lambda _:(lt O (S n)).(refl_equal bool true)) (\lambda n0:nat.(\lambda _:((lt n0 (S n))\to (eq bool 
+match n0 return (\lambda n1:nat.bool) with 
+ [ O => true
+ | (S (m:nat)) => (blt m n)
+] true)).(\lambda H1:(lt (S n0) (S n)).(H n0 (le_S_n (S n0) n H1))))) y)))) x))
+Post Nodes: 272
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_bge
+Pre Nodes : 255
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((le n y)\to (eq bool (blt y n) false)))) (\lambda y:nat.(\lambda _:(le O y).(refl_equal bool false))) (\lambda n:nat.(\lambda H:(\forall y:nat.((le n y)\to (eq bool (blt y n) false))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((le (S n) n0)\to (eq bool (blt n0 (S n)) false))) (\lambda H0:(le (S n) O). let H1 \def (le_ind (S n) (\lambda n0:nat.((eq nat n0 O)\to (eq bool (blt O (S n)) false))) (\lambda H1:(eq nat (S n) O). let H2 \def (eq_ind nat (S n) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in (False_ind (eq bool (blt O (S n)) false) H2)) (\lambda m:nat.(\lambda H1:(le (S n) m).(\lambda _:((eq nat m O)\to (eq bool (blt O (S n)) false)).(\lambda H2:(eq nat (S m) O). let H3 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H2) in  let DEFINED \def (False_ind ((le (S n) m)\to (eq bool (blt O (S n)) false)) H3) in (DEFINED H1))))) O H0) in (H1 (refl_equal nat O))) (\lambda n0:nat.(\lambda _:((le (S n) n0)\to (eq bool (blt n0 (S n)) false)).(\lambda H1:(le (S n) (S n0)).(H n0 (le_S_n n n0 H1))))) y)))) x))
+Post Nodes: 272
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: blt_lt
+Pre Nodes : 221
+bool
+bool
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((eq bool (blt y n) true)\to (lt y n)))) (\lambda y:nat.(\lambda H:(eq bool (blt y O) true). let H0 \def (eq_ind bool (blt y O) (\lambda b:bool.((eq bool b true)\to (lt y O))) (\lambda H0:(eq bool (blt y O) true). let H1 \def (eq_ind bool (blt y O) (\lambda e:bool.
+match e return (\lambda _:bool.Prop) with 
+ [ true => False
+ | false => True
+]) I true H0) in (False_ind (lt y O) H1)) true H) in (H0 (refl_equal bool true)))) (\lambda n:nat.(\lambda H:(\forall y:nat.((eq bool (blt y n) true)\to (lt y n))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((eq bool (blt n0 (S n)) true)\to (lt n0 (S n)))) (\lambda _:(eq bool true true).(le_S_n (S O) (S n) (le_n_S (S O) (S n) (le_n_S O n (le_O_n n))))) (\lambda n0:nat.(\lambda _:((eq bool 
+match n0 return (\lambda n1:nat.bool) with 
+ [ O => true
+ | (S (m:nat)) => (blt m n)
+] true)\to (lt n0 (S n))).(\lambda H1:(eq bool (blt n0 n) true).(lt_le_S (S n0) (S n) (lt_n_S n0 n (H n0 H1)))))) y)))) x))
+Post Nodes: 219
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: bge_le
+Pre Nodes : 222
+bool
+bool
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((eq bool (blt y n) false)\to (le n y)))) (\lambda y:nat.(\lambda _:(eq bool (blt y O) false).(le_O_n y))) (\lambda n:nat.(\lambda H:(\forall y:nat.((eq bool (blt y n) false)\to (le n y))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((eq bool (blt n0 (S n)) false)\to (le (S n) n0))) (\lambda H0:(eq bool (blt O (S n)) false). let H1 \def (eq_ind bool (blt O (S n)) (\lambda b:bool.((eq bool b false)\to (le (S n) O))) (\lambda H1:(eq bool (blt O (S n)) false). let H2 \def (eq_ind bool (blt O (S n)) (\lambda e:bool.
+match e return (\lambda _:bool.Prop) with 
+ [ true => True
+ | false => False
+]) I false H1) in (False_ind (le (S n) O) H2)) false H0) in (H1 (refl_equal bool false))) (\lambda n0:nat.(\lambda _:((eq bool (blt n0 (S n)) false)\to (le (S n) n0)).(\lambda H1:(eq bool (blt (S n0) (S n)) false).(le_S_n (S n) (S n0) (le_n_S (S n) (S n0) (le_n_S n n0 (H n0 H1))))))) y)))) x))
+Post Nodes: 220
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./blt/props.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of blt/props.mma completed in 7''.
+\e[0;32mInfo:  \e[0mexecution of ext/arith.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/ext ...''
+\e[0;32mInfo:  \e[0mbaseuri cic:/matita/LAMBDA-TYPES/Base-2/ext/arith is not empty
+\e[0;32mInfo:  \e[0mcleaning baseuri cic:/matita/LAMBDA-TYPES/Base-2/ext/arith
+\e[0;32mInfo:  \e[0mRemoving: cic:/matita/LAMBDA-TYPES/Base-2/ext/arith/*
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: nat_dec
+Pre Nodes : 474
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda n1:nat.(nat_ind (\lambda n:nat.(\forall n2:nat.(or (eq nat n n2) ((eq nat n n2)\to (\forall P:Prop.P))))) (\lambda n2:nat.(nat_ind (\lambda n:nat.(or (eq nat O n) ((eq nat O n)\to (\forall P:Prop.P)))) (or_introl (eq nat O O) ((eq nat O O)\to (\forall P:Prop.P)) (refl_equal nat O)) (\lambda n3:nat.(\lambda _:(or (eq nat O n3) ((eq nat O n3)\to (\forall P:Prop.P))).(or_intror (eq nat O (S n3)) ((eq nat O (S n3))\to (\forall P:Prop.P)) (\lambda H0:(eq nat O (S n3)).(\lambda P:Prop. let H1 \def (eq_ind nat O (\lambda ee:nat.
+match ee return (\lambda _:nat.Prop) with 
+ [ O => True
+ | (S (_:nat)) => False
+]) I (S n3) H0) in (False_ind P H1)))))) n2)) (\lambda n2:nat.(\lambda H:(\forall n2:nat.(or (eq nat n2 n2) ((eq nat n2 n2)\to (\forall P:Prop.P)))).(\lambda n3:nat.(nat_ind (\lambda n0:nat.(or (eq nat (S n2) n0) ((eq nat (S n2) n0)\to (\forall P:Prop.P)))) (or_intror (eq nat (S n2) O) ((eq nat (S n2) O)\to (\forall P:Prop.P)) (\lambda H0:(eq nat (S n2) O).(\lambda P:Prop. let H1 \def (eq_ind nat (S n2) (\lambda ee:nat.
+match ee return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H0) in (False_ind P H1)))) (\lambda n4:nat.(\lambda H0:(or (eq nat (S n2) n4) ((eq nat (S n2) n4)\to (\forall P:Prop.P))). let DEFINED \def (H n4) in (or_ind (eq nat n2 n4) ((eq nat n2 n4)\to (\forall P:Prop.P)) (or (eq nat (S n2) (S n4)) ((eq nat (S n2) (S n4))\to (\forall P:Prop.P))) (\lambda H1:(eq nat n2 n4).(eq_ind nat n2 (\lambda n3:nat.(or (eq nat (S n2) (S n3)) ((eq nat (S n2) (S n3))\to (\forall P:Prop.P)))) (or_introl (eq nat (S n2) (S n2)) ((eq nat (S n2) (S n2))\to (\forall P:Prop.P)) (refl_equal nat (S n2))) n4 H1)) (\lambda H1:((eq nat n2 n4)\to (\forall P:Prop.P)).(or_intror (eq nat (S n2) (S n4)) ((eq nat (S n2) (S n4))\to (\forall P:Prop.P)) (\lambda H2:(eq nat (S n2) (S n4)).(\lambda P:Prop. let H3 \def (f_equal nat nat (\lambda e:nat.
+match e return (\lambda _:nat.nat) with 
+ [ O => n2
+ | (S (n3:nat)) => n3
+]) (S n2) (S n4) H2) in  let H4 \def (eq_ind_r nat n4 (\lambda n3:nat.((eq nat n2 n3)\to (\forall P0:Prop.P0))) H1 n2 H3) in (H4 (refl_equal nat n2) P))))) DEFINED))) n3)))) n1))
+Post Nodes: 476
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: simpl_plus_r
+Pre Nodes : 85
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda n:nat.(\lambda m:nat.(\lambda p:nat.(\lambda H:(eq nat (plus m n) (plus p n)). let DEFINED \def (plus_comm n m) in (plus_reg_l n m p (eq_ind_r nat (plus m n) (\lambda n0:nat.(eq nat n0 (plus n p))) (eq_ind_r nat (plus p n) (\lambda n0:nat.(eq nat n0 (plus n p))) (sym_eq nat (plus n p) (plus p n) (plus_comm n p)) (plus m n) H) (plus n m) DEFINED))))))
+Post Nodes: 87
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_plus_r
+Pre Nodes : 33
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda m:nat.(\lambda n:nat. let DEFINED \def (plus_comm m n) in (eq_ind_r nat (plus n m) (\lambda n0:nat.(eq nat (minus n0 n) m)) (minus_plus n m) (plus m n) DEFINED)))
+Post Nodes: 35
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: plus_permute_2_in_3
+Pre Nodes : 117
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda z:nat. let DEFINED \def (plus_assoc_reverse x z y) in  let DEFINED0 \def (plus_comm y z) in  let DEFINED1 \def (plus_assoc_reverse x y z) in (eq_ind_r nat (plus x (plus y z)) (\lambda n:nat.(eq nat n (plus (plus x z) y))) (eq_ind_r nat (plus z y) (\lambda n:nat.(eq nat (plus x n) (plus (plus x z) y))) (eq_ind nat (plus (plus x z) y) (\lambda n:nat.(eq nat n (plus (plus x z) y))) (refl_equal nat (plus (plus x z) y)) (plus x (plus z y)) DEFINED) (plus y z) DEFINED0) (plus (plus x y) z) DEFINED1))))
+Post Nodes: 123
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: plus_permute_2_in_3_assoc
+Pre Nodes : 86
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda n:nat.(\lambda h:nat.(\lambda k:nat. let DEFINED \def (plus_assoc n k h) in  let DEFINED0 \def (plus_permute_2_in_3 n h k) in (eq_ind_r nat (plus (plus n k) h) (\lambda n0:nat.(eq nat n0 (plus n (plus k h)))) (eq_ind_r nat (plus (plus n k) h) (\lambda n0:nat.(eq nat (plus (plus n k) h) n0)) (refl_equal nat (plus (plus n k) h)) (plus n (plus k h)) DEFINED) (plus (plus n h) k) DEFINED0))))
+Post Nodes: 90
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: plus_O
+Pre Nodes : 191
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((eq nat (plus n y) O)\to (and (eq nat n O) (eq nat y O))))) (\lambda y:nat.(\lambda H:(eq nat (plus O y) O).(conj (eq nat O O) (eq nat y O) (refl_equal nat O) H))) (\lambda n:nat.(\lambda _:(\forall y:nat.((eq nat (plus n y) O)\to (and (eq nat n O) (eq nat y O)))).(\lambda y:nat.(\lambda H0:(eq nat (plus (S n) y) O). let H1 \def (eq_ind nat (plus (S n) y) (\lambda n0:nat.((eq nat n0 O)\to (and (eq nat (S n) O) (eq nat y O)))) (\lambda H1:(eq nat (plus (S n) y) O). let H2 \def (eq_ind nat (plus (S n) y) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in (False_ind (and (eq nat (S n) O) (eq nat y O)) H2)) O H0) in (H1 (refl_equal nat O)))))) x))
+Post Nodes: 189
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_Sx_SO
+Pre Nodes : 24
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat. let DEFINED \def (minus_n_O x) in (eq_ind nat x (\lambda n:nat.(eq nat n x)) (refl_equal nat x) (minus x O) DEFINED))
+Post Nodes: 26
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: eq_nat_dec
+Pre Nodes : 303
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda i:nat.(nat_ind (\lambda n:nat.(\forall j:nat.(or (not (eq nat n j)) (eq nat n j)))) (\lambda j:nat.(nat_ind (\lambda n:nat.(or (not (eq nat O n)) (eq nat O n))) (or_intror (not (eq nat O O)) (eq nat O O) (refl_equal nat O)) (\lambda n:nat.(\lambda _:(or (not (eq nat O n)) (eq nat O n)).(or_introl (not (eq nat O (S n))) (eq nat O (S n)) (O_S n)))) j)) (\lambda n:nat.(\lambda H:(\forall j:nat.(or (not (eq nat n j)) (eq nat n j))).(\lambda j:nat.(nat_ind (\lambda n0:nat.(or (not (eq nat (S n) n0)) (eq nat (S n) n0))) (or_introl (not (eq nat (S n) O)) (eq nat (S n) O) (sym_not_eq nat O (S n) (O_S n))) (\lambda n0:nat.(\lambda _:(or (not (eq nat (S n) n0)) (eq nat (S n) n0)). let DEFINED \def (H n0) in (or_ind (not (eq nat n n0)) (eq nat n n0) (or (not (eq nat (S n) (S n0))) (eq nat (S n) (S n0))) (\lambda H1:(not (eq nat n n0)).(or_introl (not (eq nat (S n) (S n0))) (eq nat (S n) (S n0)) (not_eq_S n n0 H1))) (\lambda H1:(eq nat n n0).(or_intror (not (eq nat (S n) (S n0))) (eq nat (S n) (S n0)) (f_equal nat nat S n n0 H1))) DEFINED))) j)))) i))
+Post Nodes: 305
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: neq_eq_e
+Pre Nodes : 47
+Optimized : (\lambda i:nat.(\lambda j:nat.(\lambda P:Prop.(\lambda H:((not (eq nat i j))\to P).(\lambda H0:((eq nat i j)\to P). let o \def (eq_nat_dec i j) in (or_ind (not (eq nat i j)) (eq nat i j) P H H0 o))))))
+Post Nodes: 47
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_false
+Pre Nodes : 382
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda m:nat.(nat_ind (\lambda n:nat.(\forall n0:nat.(\forall P:Prop.((le n n0)\to ((le (S n0) n)\to P))))) (\lambda n:nat.(\lambda P:Prop.(\lambda _:(le O n).(\lambda H0:(le (S n) O). let H1 \def (le_ind (S n) (\lambda n0:nat.((eq nat n0 O)\to P)) (\lambda H1:(eq nat (S n) O). let H2 \def (eq_ind nat (S n) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in (False_ind P H2)) (\lambda m0:nat.(\lambda H1:(le (S n) m0).(\lambda _:((eq nat m0 O)\to P).(\lambda H2:(eq nat (S m0) O). let H3 \def (eq_ind nat (S m0) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H2) in  let DEFINED \def (False_ind ((le (S n) m0)\to P) H3) in (DEFINED H1))))) O H0) in (H1 (refl_equal nat O)))))) (\lambda n:nat.(\lambda H:(\forall n0:nat.(\forall P:Prop.((le n n0)\to ((le (S n0) n)\to P)))).(\lambda n0:nat.(nat_ind (\lambda n1:nat.(\forall P:Prop.((le (S n) n1)\to ((le (S n1) (S n))\to P)))) (\lambda P:Prop.(\lambda H0:(le (S n) O).(\lambda _:(le (S O) (S n)). let H2 \def (le_ind (S n) (\lambda n1:nat.((eq nat n1 O)\to P)) (\lambda H2:(eq nat (S n) O). let H3 \def (eq_ind nat (S n) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H2) in (False_ind P H3)) (\lambda m0:nat.(\lambda H2:(le (S n) m0).(\lambda _:((eq nat m0 O)\to P).(\lambda H3:(eq nat (S m0) O). let H4 \def (eq_ind nat (S m0) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H3) in  let DEFINED \def (False_ind ((le (S n) m0)\to P) H4) in (DEFINED H2))))) O H0) in (H2 (refl_equal nat O))))) (\lambda n1:nat.(\lambda _:(\forall P:Prop.((le (S n) n1)\to ((le (S n1) (S n))\to P))).(\lambda P:Prop.(\lambda H1:(le (S n) (S n1)).(\lambda H2:(le (S (S n1)) (S n)). let DEFINED \def (le_S_n (S n1) n H2) in (H n1 P (le_S_n n n1 H1) DEFINED)))))) n0)))) m))
+Post Nodes: 400
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_Sx_x
+Pre Nodes : 20
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda H:(le (S x) x).(\lambda P:Prop. let H0 \def le_Sn_n in  let DEFINED \def (H0 x H) in (False_ind P DEFINED))))
+Post Nodes: 22
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_le
+Pre Nodes : 88
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.(le (minus n y) n))) (\lambda _:nat.(le_n O)) (\lambda n:nat.(\lambda H:(\forall y:nat.(le (minus n y) n)).(\lambda y:nat.(nat_ind (\lambda n0:nat.(le (minus (S n) n0) (S n))) (le_n (S n)) (\lambda n0:nat.(\lambda _:(le 
+match n0 return (\lambda n1:nat.nat) with 
+ [ O => (S n)
+ | (S (l:nat)) => (minus n l)
+] (S n)).(le_S (minus n n0) n (H n0)))) y)))) x))
+Post Nodes: 88
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_plus_minus_sym
+Pre Nodes : 45
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda n:nat.(\lambda m:nat.(\lambda H:(le n m). let DEFINED \def (plus_comm (minus m n) n) in (eq_ind_r nat (plus n (minus m n)) (\lambda n0:nat.(eq nat m n0)) (le_plus_minus n m H) (plus (minus m n) n) DEFINED))))
+Post Nodes: 47
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_minus_minus
+Pre Nodes : 84
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(le x y).(\lambda z:nat.(\lambda H0:(le y z). let DEFINED \def (le_plus_minus_r x z (le_trans x y z H H0)) in  let DEFINED0 \def (le_plus_minus_r x y H) in (plus_le_reg_l x (minus y x) (minus z x) (eq_ind_r nat y (\lambda n:nat.(le n (plus x (minus z x)))) (eq_ind_r nat z (\lambda n:nat.(le y n)) H0 (plus x (minus z x)) DEFINED) (plus x (minus y x)) DEFINED0)))))))
+Post Nodes: 88
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_minus_plus
+Pre Nodes : 505
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+Optimized : (\lambda z:nat.(nat_ind (\lambda n:nat.(\forall x:nat.((le n x)\to (\forall y:nat.(eq nat (minus (plus x y) n) (plus (minus x n) y)))))) (\lambda x:nat.(\lambda H:(le O x). let H0 \def (le_ind O (\lambda n:nat.((eq nat n x)\to (\forall y:nat.(eq nat (minus (plus x y) O) (plus (minus x O) y))))) (\lambda H0:(eq nat O x).(eq_ind nat O (\lambda n:nat.(\forall y:nat.(eq nat (minus (plus n y) O) (plus (minus n O) y)))) (\lambda y:nat.(sym_eq nat (plus (minus O O) y) (minus (plus O y) O) (minus_n_O (plus O y)))) x H0)) (\lambda m:nat.(\lambda H0:(le O m).(\lambda _:((eq nat m x)\to (\forall y:nat.(eq nat (minus (plus x y) O) (plus (minus x O) y)))).(\lambda H1:(eq nat (S m) x). let DEFINED \def (eq_ind nat (S m) (\lambda n:nat.((le O m)\to (\forall y:nat.(eq nat (minus (plus n y) O) (plus (minus n O) y))))) (\lambda _:(le O m).(\lambda y:nat.(refl_equal nat (plus (minus (S m) O) y)))) x H1) in (DEFINED H0))))) x H) in (H0 (refl_equal nat x)))) (\lambda z0:nat.(\lambda H:(\forall x:nat.((le z0 x)\to (\forall y:nat.(eq nat (minus (plus x y) z0) (plus (minus x z0) y))))).(\lambda x:nat.(nat_ind (\lambda n:nat.((le (S z0) n)\to (\forall y:nat.(eq nat (minus (plus n y) (S z0)) (plus (minus n (S z0)) y))))) (\lambda H0:(le (S z0) O).(\lambda y:nat. let H1 \def (le_ind (S z0) (\lambda n:nat.((eq nat n O)\to (eq nat (minus (plus O y) (S z0)) (plus (minus O (S z0)) y)))) (\lambda H1:(eq nat (S z0) O). let H2 \def (eq_ind nat (S z0) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in (False_ind (eq nat (minus (plus O y) (S z0)) (plus (minus O (S z0)) y)) H2)) (\lambda m:nat.(\lambda H1:(le (S z0) m).(\lambda _:((eq nat m O)\to (eq nat (minus (plus O y) (S z0)) (plus (minus O (S z0)) y))).(\lambda H2:(eq nat (S m) O). let H3 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H2) in  let DEFINED \def (False_ind ((le (S z0) m)\to (eq nat (minus (plus O y) (S z0)) (plus (minus O (S z0)) y))) H3) in (DEFINED H1))))) O H0) in (H1 (refl_equal nat O)))) (\lambda n:nat.(\lambda _:((le (S z0) n)\to (\forall y:nat.(eq nat (minus (plus n y) (S z0)) (plus (minus n (S z0)) y)))).(\lambda H1:(le (S z0) (S n)).(\lambda y:nat.(H n (le_S_n z0 n H1) y))))) x)))) z))
+Post Nodes: 560
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_minus
+Pre Nodes : 51
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda z:nat.(\lambda y:nat.(\lambda H:(le (plus x y) z). let DEFINED \def (minus_plus_r x y) in (eq_ind nat (minus (plus x y) y) (\lambda n:nat.(le n (minus z y))) (le_minus_minus y (plus x y) (le_plus_r x y) z H) x DEFINED)))))
+Post Nodes: 53
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_trans_plus_r
+Pre Nodes : 27
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda z:nat.(\lambda H:(le (plus x y) z).(le_trans y (plus x y) z (le_plus_r x y) H)))))
+Post Nodes: 27
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_gen_S
+Pre Nodes : 217
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+Optimized : (\lambda m:nat.(\lambda x:nat.(\lambda H:(le (S m) x). let H0 \def (le_ind (S m) (\lambda n:nat.((eq nat n x)\to (ex2 nat (\lambda n0:nat.(eq nat x (S n0))) (\lambda n0:nat.(le m n0))))) (\lambda H0:(eq nat (S m) x).(eq_ind nat (S m) (\lambda n:nat.(ex2 nat (\lambda n0:nat.(eq nat n (S n0))) (\lambda n0:nat.(le m n0)))) (ex_intro2 nat (\lambda n:nat.(eq nat (S m) (S n))) (\lambda n:nat.(le m n)) m (refl_equal nat (S m)) (le_n m)) x H0)) (\lambda m0:nat.(\lambda H0:(le (S m) m0).(\lambda _:((eq nat m0 x)\to (ex2 nat (\lambda n0:nat.(eq nat x (S n0))) (\lambda n0:nat.(le m n0)))).(\lambda H1:(eq nat (S m0) x). let DEFINED \def (eq_ind nat (S m0) (\lambda n:nat.((le (S m) m0)\to (ex2 nat (\lambda n0:nat.(eq nat n (S n0))) (\lambda n0:nat.(le m n0))))) (\lambda H2:(le (S m) m0).(ex_intro2 nat (\lambda n:nat.(eq nat (S m0) (S n))) (\lambda n:nat.(le m n)) m0 (refl_equal nat (S m0)) (le_S_n m m0 (le_S (S m) m0 H2)))) x H1) in (DEFINED H0))))) x H) in (H0 (refl_equal nat x)))))
+Post Nodes: 243
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_x_plus_x_Sy
+Pre Nodes : 64
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat. let DEFINED \def (plus_comm x (S y)) in (eq_ind_r nat (plus (S y) x) (\lambda n:nat.(lt x n)) (le_S_n (S x) (S (plus y x)) (le_n_S (S x) (S (plus y x)) (le_n_S x (plus y x) (le_plus_r y x)))) (plus x (S y)) DEFINED)))
+Post Nodes: 66
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: simpl_lt_plus_r
+Pre Nodes : 75
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda p:nat.(\lambda n:nat.(\lambda m:nat.(\lambda H:(lt (plus n p) (plus m p)). let DEFINED \def (plus_comm n p) in  let H0 \def (eq_ind nat (plus n p) (\lambda n0:nat.(lt n0 (plus m p))) H (plus p n) DEFINED) in  let DEFINED0 \def (plus_comm m p) in  let H1 \def (eq_ind nat (plus m p) (\lambda n0:nat.(lt (plus p n) n0)) H0 (plus p m) DEFINED0) in (plus_lt_reg_l n m p H1)))))
+Post Nodes: 79
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_x_Sy
+Pre Nodes : 330
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((lt y n)\to (eq nat (minus n y) (S (minus n (S y))))))) (\lambda y:nat.(\lambda H:(lt y O). let H0 \def (le_ind (S y) (\lambda n:nat.((eq nat n O)\to (eq nat (minus O y) (S (minus O (S y)))))) (\lambda H0:(eq nat (S y) O). let H1 \def (eq_ind nat (S y) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H0) in (False_ind (eq nat (minus O y) (S (minus O (S y)))) H1)) (\lambda m:nat.(\lambda H0:(le (S y) m).(\lambda _:((eq nat m O)\to (eq nat (minus O y) (S (minus O (S y))))).(\lambda H1:(eq nat (S m) O). let H2 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in  let DEFINED \def (False_ind ((le (S y) m)\to (eq nat (minus O y) (S (minus O (S y))))) H2) in (DEFINED H0))))) O H) in (H0 (refl_equal nat O)))) (\lambda n:nat.(\lambda H:(\forall y:nat.((lt y n)\to (eq nat (minus n y) (S (minus n (S y)))))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((lt n0 (S n))\to (eq nat (minus (S n) n0) (S (minus (S n) (S n0)))))) (\lambda _:(lt O (S n)). let DEFINED \def (minus_n_O n) in (eq_ind nat n (\lambda n0:nat.(eq nat (S n) (S n0))) (refl_equal nat (S n)) (minus n O) DEFINED)) (\lambda n0:nat.(\lambda _:((lt n0 (S n))\to (eq nat (minus (S n) n0) (S (minus (S n) (S n0))))).(\lambda H1:(lt (S n0) (S n)). let H2 \def (le_S_n (S n0) n H1) in (H n0 H2)))) y)))) x))
+Post Nodes: 354
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_plus_minus
+Pre Nodes : 16
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(lt x y).(le_plus_minus (S x) y H))))
+Post Nodes: 16
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_plus_minus_r
+Pre Nodes : 53
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(lt x y). let DEFINED \def (plus_comm (minus y (S x)) x) in (eq_ind_r nat (plus x (minus y (S x))) (\lambda n:nat.(eq nat y (S n))) (lt_plus_minus x y H) (plus (minus y (S x)) x) DEFINED))))
+Post Nodes: 55
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_x_SO
+Pre Nodes : 56
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda H:(lt O x). let DEFINED \def (minus_n_O x) in  let DEFINED0 \def (minus_x_Sy x O H) in (eq_ind nat (minus x O) (\lambda n:nat.(eq nat x n)) (eq_ind nat x (\lambda n:nat.(eq nat x n)) (refl_equal nat x) (minus x O) DEFINED) (S (minus x (S O))) DEFINED0)))
+Post Nodes: 60
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_x_pred_y
+Pre Nodes : 175
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+Optimized : (\lambda y:nat.(nat_ind (\lambda n:nat.(\forall x:nat.((lt x n)\to (le x (pred n))))) (\lambda x:nat.(\lambda H:(lt x O). let H0 \def (le_ind (S x) (\lambda n:nat.((eq nat n O)\to (le x O))) (\lambda H0:(eq nat (S x) O). let H1 \def (eq_ind nat (S x) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H0) in (False_ind (le x O) H1)) (\lambda m:nat.(\lambda H0:(le (S x) m).(\lambda _:((eq nat m O)\to (le x O)).(\lambda H1:(eq nat (S m) O). let H2 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in  let DEFINED \def (False_ind ((le (S x) m)\to (le x O)) H2) in (DEFINED H0))))) O H) in (H0 (refl_equal nat O)))) (\lambda n:nat.(\lambda _:(\forall x:nat.((lt x n)\to (le x (pred n)))).(\lambda x:nat.(\lambda H0:(lt x (S n)).(le_S_n x n H0))))) y))
+Post Nodes: 186
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_le_minus
+Pre Nodes : 44
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(lt x y). let DEFINED \def (plus_comm x (S O)) in (le_minus x y (S O) (eq_ind_r nat (plus (S O) x) (\lambda n:nat.(le n y)) H (plus x (S O)) DEFINED)))))
+Post Nodes: 46
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_le_e
+Pre Nodes : 39
+Optimized : (\lambda n:nat.(\lambda d:nat.(\lambda P:Prop.(\lambda H:((lt n d)\to P).(\lambda H0:((le d n)\to P). let H1 \def (le_or_lt d n) in (or_ind (le d n) (lt n d) P H0 H H1))))))
+Post Nodes: 39
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_eq_e
+Pre Nodes : 45
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda P:Prop.(\lambda H:((lt x y)\to P).(\lambda H0:((eq nat x y)\to P).(\lambda H1:(le x y). let DEFINED \def (le_lt_or_eq x y H1) in (or_ind (lt x y) (eq nat x y) P H H0 DEFINED)))))))
+Post Nodes: 47
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_eq_gt_e
+Pre Nodes : 60
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda P:Prop.(\lambda H:((lt x y)\to P).(\lambda H0:((eq nat x y)\to P).(\lambda H1:((lt y x)\to P).(lt_le_e x y P H (\lambda H2:(le y x).(lt_eq_e y x P H1 (\lambda H3:(eq nat y x).(H0 (sym_eq nat y x H3))) H2)))))))))
+Post Nodes: 60
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_gen_xS
+Pre Nodes : 190
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall n0:nat.((lt n (S n0))\to (or (eq nat n O) (ex2 nat (\lambda m:nat.(eq nat n (S m))) (\lambda m:nat.(lt m n0))))))) (\lambda n:nat.(\lambda _:(lt O (S n)).(or_introl (eq nat O O) (ex2 nat (\lambda m:nat.(eq nat O (S m))) (\lambda m:nat.(lt m n))) (refl_equal nat O)))) (\lambda n:nat.(\lambda _:(\forall n0:nat.((lt n (S n0))\to (or (eq nat n O) (ex2 nat (\lambda m:nat.(eq nat n (S m))) (\lambda m:nat.(lt m n0)))))).(\lambda n0:nat.(\lambda H0:(lt (S n) (S n0)).(or_intror (eq nat (S n) O) (ex2 nat (\lambda m:nat.(eq nat (S n) (S m))) (\lambda m:nat.(lt m n0))) (ex_intro2 nat (\lambda m:nat.(eq nat (S n) (S m))) (\lambda m:nat.(lt m n0)) n (refl_equal nat (S n)) (le_S_n (S n) n0 H0))))))) x))
+Post Nodes: 190
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_lt_false
+Pre Nodes : 25
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(le x y).(\lambda H0:(lt y x).(\lambda P:Prop. let DEFINED \def (le_not_lt x y H H0) in (False_ind P DEFINED))))))
+Post Nodes: 27
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: lt_neq
+Pre Nodes : 33
+Optimized : (\lambda x:nat.(\lambda y:nat.(\lambda H:(lt x y).(\lambda H0:(eq nat x y). let H1 \def (eq_ind nat x (\lambda n:nat.(lt n y)) H y H0) in (lt_irrefl y H1)))))
+Post Nodes: 33
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: arith0
+Pre Nodes : 185
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda h2:nat.(\lambda d2:nat.(\lambda n:nat.(\lambda H:(le (plus d2 h2) n).(\lambda h3:nat. let DEFINED \def (plus_comm h2 d2) in  let DEFINED0 \def (plus_assoc h2 d2 h3) in  let DEFINED1 \def (minus_plus h2 (plus d2 h3)) in (eq_ind nat (minus (plus h2 (plus d2 h3)) h2) (\lambda n0:nat.(le n0 (minus (plus n h3) h2))) (le_minus_minus h2 (plus h2 (plus d2 h3)) (le_plus_l h2 (plus d2 h3)) (plus n h3) (eq_ind_r nat (plus (plus h2 d2) h3) (\lambda n0:nat.(le n0 (plus n h3))) (eq_ind_r nat (plus d2 h2) (\lambda n0:nat.(le (plus n0 h3) (plus n h3))) (le_S_n (plus (plus d2 h2) h3) (plus n h3) (lt_le_S (plus (plus d2 h2) h3) (S (plus n h3)) (le_lt_n_Sm (plus (plus d2 h2) h3) (plus n h3) (plus_le_compat (plus d2 h2) n h3 h3 H (le_n h3))))) (plus h2 d2) DEFINED) (plus h2 (plus d2 h3)) DEFINED0)) (plus d2 h3) DEFINED1))))))
+Post Nodes: 191
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: O_minus
+Pre Nodes : 211
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((le n y)\to (eq nat (minus n y) O)))) (\lambda y:nat.(\lambda _:(le O y).(refl_equal nat O))) (\lambda x0:nat.(\lambda H:(\forall y:nat.((le x0 y)\to (eq nat (minus x0 y) O))).(\lambda y:nat.(nat_ind (\lambda n:nat.((le (S x0) n)\to (eq nat 
+match n return (\lambda n1:nat.nat) with 
+ [ O => (S x0)
+ | (S (l:nat)) => (minus x0 l)
+] O))) (\lambda H0:(le (S x0) O). let DEFINED \def (le_gen_S x0 O H0) in (ex2_ind nat (\lambda n:nat.(eq nat O (S n))) (\lambda n:nat.(le x0 n)) (eq nat (S x0) O) (\lambda x1:nat.(\lambda H1:(eq nat O (S x1)).(\lambda _:(le x0 x1). let H3 \def (eq_ind nat O (\lambda ee:nat.
+match ee return (\lambda _:nat.Prop) with 
+ [ O => True
+ | (S (_:nat)) => False
+]) I (S x1) H1) in (False_ind (eq nat (S x0) O) H3)))) DEFINED)) (\lambda n:nat.(\lambda _:((le (S x0) n)\to (eq nat 
+match n return (\lambda n1:nat.nat) with 
+ [ O => (S x0)
+ | (S (l:nat)) => (minus x0 l)
+] O)).(\lambda H1:(le (S x0) (S n)).(H n (le_S_n x0 n H1))))) y)))) x))
+Post Nodes: 213
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_minus
+Pre Nodes : 592
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda z:nat.(nat_ind (\lambda n:nat.(\forall x:nat.(\forall y:nat.((le n x)\to ((le n y)\to ((eq nat (minus x n) (minus y n))\to (eq nat x y))))))) (\lambda x:nat.(\lambda y:nat.(\lambda _:(le O x).(\lambda _:(le O y).(\lambda H1:(eq nat (minus x O) (minus y O)). let DEFINED \def (minus_n_O x) in  let H2 \def (eq_ind_r nat (minus x O) (\lambda n:nat.(eq nat n (minus y O))) H1 x DEFINED) in  let DEFINED0 \def (minus_n_O y) in  let H3 \def (eq_ind_r nat (minus y O) (\lambda n:nat.(eq nat x n)) H2 y DEFINED0) in H3))))) (\lambda z0:nat.(\lambda IH:(\forall x:nat.(\forall y:nat.((le z0 x)\to ((le z0 y)\to ((eq nat (minus x z0) (minus y z0))\to (eq nat x y)))))).(\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((le (S z0) n)\to ((le (S z0) y)\to ((eq nat (minus n (S z0)) (minus y (S z0)))\to (eq nat n y)))))) (\lambda y:nat.(\lambda H:(le (S z0) O).(\lambda _:(le (S z0) y).(\lambda _:(eq nat (minus O (S z0)) (minus y (S z0))). let DEFINED \def (le_gen_S z0 O H) in (ex2_ind nat (\lambda n:nat.(eq nat O (S n))) (\lambda n:nat.(le z0 n)) (eq nat O y) (\lambda x0:nat.(\lambda H2:(eq nat O (S x0)).(\lambda _:(le z0 x0). let H4 \def (eq_ind nat O (\lambda ee:nat.
+match ee return (\lambda _:nat.Prop) with 
+ [ O => True
+ | (S (_:nat)) => False
+]) I (S x0) H2) in (False_ind (eq nat O y) H4)))) DEFINED))))) (\lambda x0:nat.(\lambda _:(\forall y:nat.((le (S z0) x0)\to ((le (S z0) y)\to ((eq nat (minus x0 (S z0)) (minus y (S z0)))\to (eq nat x0 y))))).(\lambda y:nat.(nat_ind (\lambda n:nat.((le (S z0) (S x0))\to ((le (S z0) n)\to ((eq nat (minus (S x0) (S z0)) (minus n (S z0)))\to (eq nat (S x0) n))))) (\lambda _:(le (S z0) (S x0)).(\lambda H0:(le (S z0) O).(\lambda _:(eq nat (minus (S x0) (S z0)) (minus O (S z0))). let DEFINED \def (le_gen_S z0 O H0) in (ex2_ind nat (\lambda n:nat.(eq nat O (S n))) (\lambda n:nat.(le z0 n)) (eq nat (S x0) O) (\lambda x1:nat.(\lambda H2:(eq nat O (S x1)).(\lambda _:(le z0 x1). let H4 \def (eq_ind nat O (\lambda ee:nat.
+match ee return (\lambda _:nat.Prop) with 
+ [ O => True
+ | (S (_:nat)) => False
+]) I (S x1) H2) in (False_ind (eq nat (S x0) O) H4)))) DEFINED)))) (\lambda y0:nat.(\lambda _:((le (S z0) (S x0))\to ((le (S z0) y0)\to ((eq nat (minus (S x0) (S z0)) (minus y0 (S z0)))\to (eq nat (S x0) y0)))).(\lambda H:(le (S z0) (S x0)).(\lambda H0:(le (S z0) (S y0)).(\lambda H1:(eq nat (minus (S x0) (S z0)) (minus (S y0) (S z0))).(f_equal nat nat S x0 y0 (IH x0 y0 (le_S_n z0 x0 H) (le_S_n z0 y0 H0) H1))))))) y)))) x)))) z))
+Post Nodes: 600
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: plus_plus
+Pre Nodes : 1222
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 1
+Optimized : (\lambda z:nat.(nat_ind (\lambda n:nat.(\forall x1:nat.(\forall x2:nat.(\forall y1:nat.(\forall y2:nat.((le x1 n)\to ((le x2 n)\to ((eq nat (plus (minus n x1) y1) (plus (minus n x2) y2))\to (eq nat (plus x1 y2) (plus x2 y1)))))))))) (\lambda x1:nat.(\lambda x2:nat.(\lambda y1:nat.(\lambda y2:nat.(\lambda H:(le x1 O).(\lambda H0:(le x2 O).(\lambda H1:(eq nat y1 y2). let H_y \def (le_n_O_eq x2 H0) in  let H_y0 \def (le_n_O_eq x1 H) in (eq_ind nat y1 (\lambda n:nat.(eq nat (plus x1 n) (plus x2 y1))) (eq_ind nat O (\lambda n:nat.(eq nat (plus x1 y1) (plus n y1))) (eq_ind nat O (\lambda n:nat.(eq nat (plus n y1) (plus O y1))) (refl_equal nat (plus O y1)) x1 H_y0) x2 H_y) y2 H1)))))))) (\lambda z0:nat.(\lambda IH:(\forall x1:nat.(\forall x2:nat.(\forall y1:nat.(\forall y2:nat.((le x1 z0)\to ((le x2 z0)\to ((eq nat (plus (minus z0 x1) y1) (plus (minus z0 x2) y2))\to (eq nat (plus x1 y2) (plus x2 y1))))))))).(\lambda x1:nat.(nat_ind (\lambda n:nat.(\forall x2:nat.(\forall y1:nat.(\forall y2:nat.((le n (S z0))\to ((le x2 (S z0))\to ((eq nat (plus (minus (S z0) n) y1) (plus (minus (S z0) x2) y2))\to (eq nat (plus n y2) (plus x2 y1))))))))) (\lambda x2:nat.(nat_ind (\lambda n:nat.(\forall y1:nat.(\forall y2:nat.((le O (S z0))\to ((le n (S z0))\to ((eq nat (plus (minus (S z0) O) y1) (plus (minus (S z0) n) y2))\to (eq nat (plus O y2) (plus n y1)))))))) (\lambda y1:nat.(\lambda y2:nat.(\lambda _:(le O (S z0)).(\lambda _:(le O (S z0)).(\lambda H1:(eq nat (S (plus z0 y1)) (S (plus z0 y2))). let H_y \def (IH O O) in  let DEFINED \def (minus_n_O z0) in  let H2 \def (eq_ind_r nat (minus z0 O) (\lambda n:nat.(\forall y3:nat.(\forall y4:nat.((le O z0)\to ((le O z0)\to ((eq nat (plus n y3) (plus n y4))\to (eq nat y4 y3))))))) H_y z0 DEFINED) in (H2 y1 y2 (le_O_n z0) (le_O_n z0) (H2 (plus z0 y2) (plus z0 y1) (le_O_n z0) (le_O_n z0) (f_equal nat nat (plus z0) (plus z0 y2) (plus z0 y1) (sym_eq nat (plus z0 y1) (plus z0 y2) (eq_add_S (plus z0 y1) (plus z0 y2) H1)))))))))) (\lambda x3:nat.(\lambda _:(\forall y1:nat.(\forall y2:nat.((le O (S z0))\to ((le x3 (S z0))\to ((eq nat (S (plus z0 y1)) (plus 
+match x3 return (\lambda n:nat.nat) with 
+ [ O => (S z0)
+ | (S (l:nat)) => (minus z0 l)
+] y2))\to (eq nat y2 (plus x3 y1))))))).(\lambda y1:nat.(\lambda y2:nat.(\lambda _:(le O (S z0)).(\lambda H0:(le (S x3) (S z0)).(\lambda H1:(eq nat (S (plus z0 y1)) (plus (minus z0 x3) y2)). let H_y \def (IH O x3 (S y1)) in  let DEFINED \def (minus_n_O z0) in  let H2 \def (eq_ind_r nat (minus z0 O) (\lambda n:nat.(\forall y3:nat.((le O z0)\to ((le x3 z0)\to ((eq nat (plus n (S y1)) (plus (minus z0 x3) y3))\to (eq nat y3 (plus x3 (S y1)))))))) H_y z0 DEFINED) in  let DEFINED0 \def (plus_n_Sm z0 y1) in  let H3 \def (eq_ind_r nat (plus z0 (S y1)) (\lambda n:nat.(\forall y3:nat.((le O z0)\to ((le x3 z0)\to ((eq nat n (plus (minus z0 x3) y3))\to (eq nat y3 (plus x3 (S y1)))))))) H2 (S (plus z0 y1)) DEFINED0) in  let DEFINED1 \def (plus_n_Sm x3 y1) in  let H4 \def (eq_ind_r nat (plus x3 (S y1)) (\lambda n:nat.(\forall y3:nat.((le O z0)\to ((le x3 z0)\to ((eq nat (S (plus z0 y1)) (plus (minus z0 x3) y3))\to (eq nat y3 n)))))) H3 (S (plus x3 y1)) DEFINED1) in (H4 y2 (le_O_n z0) (le_S_n x3 z0 H0) H1)))))))) x2)) (\lambda x2:nat.(\lambda _:(\forall x3:nat.(\forall y1:nat.(\forall y2:nat.((le x2 (S z0))\to ((le x3 (S z0))\to ((eq nat (plus (minus (S z0) x2) y1) (plus (minus (S z0) x3) y2))\to (eq nat (plus x2 y2) (plus x3 y1)))))))).(\lambda x3:nat.(nat_ind (\lambda n:nat.(\forall y1:nat.(\forall y2:nat.((le (S x2) (S z0))\to ((le n (S z0))\to ((eq nat (plus (minus (S z0) (S x2)) y1) (plus (minus (S z0) n) y2))\to (eq nat (plus (S x2) y2) (plus n y1)))))))) (\lambda y1:nat.(\lambda y2:nat.(\lambda H:(le (S x2) (S z0)).(\lambda _:(le O (S z0)).(\lambda H1:(eq nat (plus (minus z0 x2) y1) (S (plus z0 y2))). let H_y \def (IH x2 O y1 (S y2)) in  let DEFINED \def (minus_n_O z0) in  let H2 \def (eq_ind_r nat (minus z0 O) (\lambda n:nat.((le x2 z0)\to ((le O z0)\to ((eq nat (plus (minus z0 x2) y1) (plus n (S y2)))\to (eq nat (plus x2 (S y2)) y1))))) H_y z0 DEFINED) in  let DEFINED0 \def (plus_n_Sm z0 y2) in  let H3 \def (eq_ind_r nat (plus z0 (S y2)) (\lambda n:nat.((le x2 z0)\to ((le O z0)\to ((eq nat (plus (minus z0 x2) y1) n)\to (eq nat (plus x2 (S y2)) y1))))) H2 (S (plus z0 y2)) DEFINED0) in  let DEFINED1 \def (plus_n_Sm x2 y2) in  let H4 \def (eq_ind_r nat (plus x2 (S y2)) (\lambda n:nat.((le x2 z0)\to ((le O z0)\to ((eq nat (plus (minus z0 x2) y1) (S (plus z0 y2)))\to (eq nat n y1))))) H3 (S (plus x2 y2)) DEFINED1) in (H4 (le_S_n x2 z0 H) (le_O_n z0) H1)))))) (\lambda x4:nat.(\lambda _:(\forall y1:nat.(\forall y2:nat.((le (S x2) (S z0))\to ((le x4 (S z0))\to ((eq nat (plus (minus z0 x2) y1) (plus 
+match x4 return (\lambda n:nat.nat) with 
+ [ O => (S z0)
+ | (S (l:nat)) => (minus z0 l)
+] y2))\to (eq nat (S (plus x2 y2)) (plus x4 y1))))))).(\lambda y1:nat.(\lambda y2:nat.(\lambda H:(le (S x2) (S z0)).(\lambda H0:(le (S x4) (S z0)).(\lambda H1:(eq nat (plus (minus z0 x2) y1) (plus (minus z0 x4) y2)).(f_equal nat nat S (plus x2 y2) (plus x4 y1) (IH x2 x4 y1 y2 (le_S_n x2 z0 H) (le_S_n x4 z0 H0) H1))))))))) x3)))) x1)))) z))
+Post Nodes: 1236
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: le_S_minus
+Pre Nodes : 41
+\e[0;33mWarn:  \e[0mOptimizer: remove 1
+Optimized : (\lambda d:nat.(\lambda h:nat.(\lambda n:nat.(\lambda H:(le (plus d h) n).(le_S d (minus n h) (le_minus d n h H))))))
+Post Nodes: 27
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./ext/arith.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of ext/arith.mma completed in 44''.
+\e[0;32mInfo:  \e[0mexecution of ext/tactics.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/ext ...''
+\e[0;32mInfo:  \e[0mbaseuri cic:/matita/LAMBDA-TYPES/Base-2/ext/tactics is not empty
+\e[0;32mInfo:  \e[0mcleaning baseuri cic:/matita/LAMBDA-TYPES/Base-2/ext/tactics
+\e[0;32mInfo:  \e[0mRemoving: cic:/matita/LAMBDA-TYPES/Base-2/ext/tactics/*
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: insert_eq
+Pre Nodes : 36
+Optimized : (\lambda S:Set.(\lambda x:S.(\lambda P:(S\to Prop).(\lambda G:Prop.(\lambda H:(\forall y:S.((P y)\to ((eq S y x)\to G))).(\lambda H0:(P x).(H x H0 (refl_equal S x))))))))
+Post Nodes: 36
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: unintro
+Pre Nodes : 17
+Optimized : (\lambda A:Set.(\lambda a:A.(\lambda P:(A\to Prop).(\lambda H:(\forall x:A.(P x)).(H a)))))
+Post Nodes: 17
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: xinduction
+Pre Nodes : 27
+Optimized : (\lambda A:Set.(\lambda t:A.(\lambda P:(A\to Prop).(\lambda H:(\forall x:A.((eq A t x)\to (P x))).(H t (refl_equal A t))))))
+Post Nodes: 27
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./ext/tactics.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of ext/tactics.mma completed in 4''.
+\e[0;32mInfo:  \e[0mexecution of pippo.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/pip ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: minus_x_Sy
+Pre Nodes : 330
+nat
+nat
+nat
+nat
+\e[0;33mWarn:  \e[0mOptimizer: remove 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: nested application
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 2
+\e[0;33mWarn:  \e[0mOptimizer: swap 2
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda x:nat.(nat_ind (\lambda n:nat.(\forall y:nat.((lt y n)\to (eq nat (minus n y) (S (minus n (S y))))))) (\lambda y:nat.(\lambda H:(lt y O). let H0 \def (le_ind (S y) (\lambda n:nat.((eq nat n O)\to (eq nat (minus O y) (S (minus O (S y)))))) (\lambda H0:(eq nat (S y) O). let H1 \def (eq_ind nat (S y) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H0) in (False_ind (eq nat (minus O y) (S (minus O (S y)))) H1)) (\lambda m:nat.(\lambda H0:(le (S y) m).(\lambda _:((eq nat m O)\to (eq nat (minus O y) (S (minus O (S y))))).(\lambda H1:(eq nat (S m) O). let H2 \def (eq_ind nat (S m) (\lambda e:nat.
+match e return (\lambda _:nat.Prop) with 
+ [ O => False
+ | (S (_:nat)) => True
+]) I O H1) in  let DEFINED \def (False_ind ((le (S y) m)\to (eq nat (minus O y) (S (minus O (S y))))) H2) in (DEFINED H0))))) O H) in (H0 (refl_equal nat O)))) (\lambda n:nat.(\lambda H:(\forall y:nat.((lt y n)\to (eq nat (minus n y) (S (minus n (S y)))))).(\lambda y:nat.(nat_ind (\lambda n0:nat.((lt n0 (S n))\to (eq nat (minus (S n) n0) (S (minus (S n) (S n0)))))) (\lambda _:(lt O (S n)). let DEFINED \def (minus_n_O n) in (eq_ind nat n (\lambda n0:nat.(eq nat (S n) (S n0))) (refl_equal nat (S n)) (minus n O) DEFINED)) (\lambda n0:nat.(\lambda _:((lt n0 (S n))\to (eq nat (minus (S n) n0) (S (minus (S n) (S n0))))).(\lambda H1:(lt (S n0) (S n)). let H2 \def (le_S_n (S n0) n H1) in (H n0 H2)))) y)))) x))
+Post Nodes: 354
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./pippo.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of pippo.mma completed in 2''.
+\e[0;32mInfo:  \e[0mexecution of plist/defs.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/pli ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./plist/defs.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of plist/defs.mma completed in 1''.
+\e[0;32mInfo:  \e[0mexecution of plist/props.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/pli ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./plist/defs.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/plist/def ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: papp_ss
+Pre Nodes : 121
+\e[0;33mWarn:  \e[0mOptimizer: anticipate 3
+\e[0;33mWarn:  \e[0mOptimizer: swap 3
+Optimized : (\lambda is1:PList.(PList_ind (\lambda p:PList.(\forall is2:PList.(eq PList (papp (Ss p) (Ss is2)) (Ss (papp p is2))))) (\lambda is2:PList.(refl_equal PList (Ss is2))) (\lambda n:nat.(\lambda n0:nat.(\lambda p:PList.(\lambda H:(\forall is2:PList.(eq PList (papp (Ss p) (Ss is2)) (Ss (papp p is2)))).(\lambda is2:PList. let DEFINED \def (H is2) in (eq_ind_r PList (Ss (papp p is2)) (\lambda p0:PList.(eq PList (PCons n (S n0) p0) (PCons n (S n0) (Ss (papp p is2))))) (refl_equal PList (PCons n (S n0) (Ss (papp p is2)))) (papp (Ss p) (Ss is2)) DEFINED)))))) is1))
+Post Nodes: 123
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./plist/props.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of plist/props.mma completed in 2''.
+\e[0;32mInfo:  \e[0mexecution of types/defs.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/typ ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./preamble.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/preamble" ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./types/defs.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of types/defs.mma completed in 0''.
+\e[0;32mInfo:  \e[0mexecution of types/props.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/typ ...''
+\e[0;32mInfo:  \e[0mbaseuri cic:/matita/LAMBDA-TYPES/Base-2/types/props is not empty
+\e[0;32mInfo:  \e[0mcleaning baseuri cic:/matita/LAMBDA-TYPES/Base-2/types/props
+\e[0;32mInfo:  \e[0mRemoving: cic:/matita/LAMBDA-TYPES/Base-2/types/props/*
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./types/defs.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/types/def ...''
+\e[0;34mDebug: \e[0mExecuting: ``inline procedural "cic:/matita/LAMBDA-TYPES/Base-1 ...''
+BEGIN: ex2_sym
+Pre Nodes : 77
+Optimized : (\lambda A:Set.(\lambda P:(A\to Prop).(\lambda Q:(A\to Prop).(\lambda H:(ex2 A (\lambda x:A.(P x)) (\lambda x:A.(Q x))).(ex2_ind A (\lambda x:A.(P x)) (\lambda x:A.(Q x)) (ex2 A (\lambda x:A.(Q x)) (\lambda x:A.(P x))) (\lambda x:A.(\lambda H0:(P x).(\lambda H1:(Q x).(ex_intro2 A (\lambda x0:A.(Q x0)) (\lambda x0:A.(P x0)) x H1 H0)))) H)))))
+Post Nodes: 77
+\e[0;34mDebug: \e[0mProcedural: level 2 transformation
+\e[0;34mDebug: \e[0mProcedural: grafite rendering
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./types/props.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of types/props.mma completed in 2''.
+\e[0;32mInfo:  \e[0mexecution of theory.mma started:
+\e[0;34mDebug: \e[0mExecuting: ``set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/the ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./ext/tactics.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/ext/tacti ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./ext/arith.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/ext/arith ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./types/props.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/types/pro ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./blt/props.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/blt/props ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./plist/props.ma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;34mDebug: \e[0mExecuting: ``include "cic:/matita/LAMBDA-TYPES/Base-2/plist/pro ...''
+\e[0;34mDebug: \e[0mIncluding /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/./theory.mma with path: /home/fguidi/svn/software/matita/contribs/LAMBDA-TYPES/Base-2/.
+\e[0;32mInfo:  \e[0mexecution of theory.mma completed in 1''.

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/makefile b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/makefile
new file mode 100644 (file)
index 0000000..7615bb7
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/makefile
@@ -0,0 +1,51 @@
+H=@
+
+RT_BASEDIR=/home/fguidi/svn/software/matita/
+OPTIONS=-bench
+MMAKE=$(RT_BASEDIR)matitamake $(OPTIONS)
+CLEAN=$(RT_BASEDIR)matitaclean $(OPTIONS) 
+MMAKEO=$(RT_BASEDIR)matitamake.opt $(OPTIONS)
+CLEANO=$(RT_BASEDIR)matitaclean.opt $(OPTIONS) 
+
+devel:=$(shell basename `pwd`)
+
+ifneq "$(SRC)" ""
+  XXX="SRC=$(SRC)"
+endif
+
+all: build_mas preall 
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) build $(devel)
+clean: clean_mas preall
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) clean $(devel)
+cleanall: clean_mas preall
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MCLEAN) all
+
+all.opt opt: build_mas preall.opt
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) build $(devel)
+clean.opt: clean_mas preall.opt
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) clean $(devel)
+cleanall.opt: clean_mas preall.opt
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MCLEANO) all
+
+%.mo: preall
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) $@
+%.mo.opt: preall.opt
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) $(@:.opt=)
+       
+preall:
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) init $(devel)
+
+preall.opt:
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) init $(devel)
+
+
+# FG: added part ############################################################
+
+build_mas:
+       $(H)$(MAKE) preamble.mo.opt
+       $(H)$(MAKE) -f Makefile
+       $(H)$(MAKE) preall.opt
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) clean $(devel)
+
+clean_mas:
+       $(H)$(MAKE) -f Makefile clean

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/defs.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/defs.mma
new file mode 100644 (file)
index 0000000..a1b6cdf
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/defs.mma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/plist/defs".
+
+include "preamble.ma".
+
+(* object PList not inlined *)
+
+
+(* object PConsTail not inlined *)
+
+
+(* object Ss not inlined *)
+
+
+(* object papp not inlined *)
+
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/props.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/props.mma
new file mode 100644 (file)
index 0000000..29357a8
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/plist/props.mma
@@ -0,0 +1,22 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/plist/props".
+
+include "plist/defs.ma".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/plist/props/papp_ss.con".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/preamble.ma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/preamble.ma
new file mode 100644 (file)
index 0000000..84a4955
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/preamble.ma
@@ -0,0 +1,32 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/preamble".
+
+include "../Base-1/definitions.ma".
+
+alias id "le_ind" = "cic:/Coq/Init/Peano/le_ind.con".
+
+default "equality"
+ cic:/Coq/Init/Logic/eq.ind
+ cic:/matita/LAMBDA-TYPES/Base-1/preamble/sym_eq.con
+ cic:/matita/LAMBDA-TYPES/Base-1/preamble/trans_eq.con
+ cic:/Coq/Init/Logic/eq_ind.con
+ cic:/Coq/Init/Logic/eq_ind_r.con
+ cic:/Coq/Init/Logic/eq_rec.con
+ cic:/Coq/Init/Logic/eq_rec_r.con
+ cic:/Coq/Init/Logic/eq_rect.con
+ cic:/Coq/Init/Logic/eq_rect_r.con
+ cic:/matita/LAMBDA-TYPES/Base-1/preamble/f_equal.con
+ cic:/matita/legacy/coq/f_equal1.con.

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/theory.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/theory.mma
new file mode 100644 (file)
index 0000000..1adab3e
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/theory.mma
@@ -0,0 +1,28 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/theory".
+
+include "ext/tactics.ma".
+
+include "ext/arith.ma".
+
+include "types/props.ma".
+
+include "blt/props.ma".
+
+include "plist/props.ma".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/defs.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/defs.mma
new file mode 100644 (file)
index 0000000..cad4f80
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/defs.mma
@@ -0,0 +1,77 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/types/defs".
+
+include "preamble.ma".
+
+(* object and3 not inlined *)
+
+
+(* object or3 not inlined *)
+
+
+(* object or4 not inlined *)
+
+
+(* object ex3 not inlined *)
+
+
+(* object ex4 not inlined *)
+
+
+(* object ex_2 not inlined *)
+
+
+(* object ex2_2 not inlined *)
+
+
+(* object ex3_2 not inlined *)
+
+
+(* object ex4_2 not inlined *)
+
+
+(* object ex_3 not inlined *)
+
+
+(* object ex2_3 not inlined *)
+
+
+(* object ex3_3 not inlined *)
+
+
+(* object ex4_3 not inlined *)
+
+
+(* object ex3_4 not inlined *)
+
+
+(* object ex4_4 not inlined *)
+
+
+(* object ex4_5 not inlined *)
+
+
+(* object ex5_5 not inlined *)
+
+
+(* object ex6_6 not inlined *)
+
+
+(* object ex6_7 not inlined *)
+
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/props.mma b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/props.mma
new file mode 100644 (file)
index 0000000..d79bfc4
--- /dev/null
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Base-2/types/props.mma
@@ -0,0 +1,22 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* This file was automatically generated: do not edit *********************)
+
+set "baseuri" "cic:/matita/LAMBDA-TYPES/Base-2/types/props".
+
+include "types/defs.ma".
+
+inline procedural "cic:/matita/LAMBDA-TYPES/Base-1/types/props/ex2_sym.con".
+

diff --git a/helm/software/matita/contribs/LAMBDA-TYPES/Makefile b/helm/software/matita/contribs/LAMBDA-TYPES/Makefile
index 285c55b99f427f4cb8c5b90cb3394d4f22dbec1d..8faf376f1732d3e29b5ad46dc494d96ac7ccfd2f 100644 (file)
--- a/helm/software/matita/contribs/LAMBDA-TYPES/Makefile
+++ b/helm/software/matita/contribs/LAMBDA-TYPES/Makefile
@@ -1,6 +1,6 @@
 GOALS = all opt clean clean.opt
 
-DEVELS = Base-1 LambdaDelta-1 Unified-Sub
+DEVELS = Base-1 LambdaDelta-1 Base-2 Unified-Sub 
 
 $(GOALS): 
        @$(foreach DEVEL, $(DEVELS), $(MAKE) -C $(DEVEL) $@;) 

diff --git a/helm/software/matita/template_makefile_devel.in b/helm/software/matita/template_makefile_devel.in
index 73996380f5c4352565d16ce8a672bc7dd3f527e0..1c0b1687b8512e86f52f4515e66f658e6f7a5f7b 100644 (file)
--- a/helm/software/matita/template_makefile_devel.in
+++ b/helm/software/matita/template_makefile_devel.in
@@ -30,7 +30,7 @@ cleanall.opt: preall.opt
 %.mo: preall
        $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) $@
 %.mo.opt: preall.opt
-       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) $@
+       $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKEO) $(@:.opt=)
        
 preall:
        $(H)$(XXX) MATITA_FLAGS=$(MATITA_FLAGS) $(MMAKE) init $(devel)