From: Cosimo Oliboni <??>
Date: Wed, 5 Aug 2009 15:02:06 +0000 (+0000)
Subject:  freescale porting, work in progress
X-Git-Tag: make_still_working~3566
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=17e7978cda0dfa4585393b0c48bd96e9504a6b92;p=helm.git

 freescale porting, work in progress
---

diff --git a/helm/software/matita/contribs/ng_assembly/compiler/ast_type.ma b/helm/software/matita/contribs/ng_assembly/compiler/ast_type.ma
new file mode 100755
index 000000000..f2bc4229f
--- /dev/null
+++ b/helm/software/matita/contribs/ng_assembly/compiler/ast_type.ma
@@ -0,0 +1,139 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it                   *)
+(*     Cosimo Oliboni, oliboni@cs.unibo.it                                *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "common/list_utility.ma".
+
+(* ************************* *)
+(* dimensioni degli elementi *)
+(* ************************* *)
+
+(* usato per definire nell'ast *)
+ninductive ast_base_type : Type ≝
+  AST_BASE_TYPE_BYTE8: ast_base_type
+| AST_BASE_TYPE_WORD16: ast_base_type
+| AST_BASE_TYPE_WORD32: ast_base_type.
+
+ninductive ast_type : Type ≝
+  AST_TYPE_BASE: ast_base_type → ast_type
+| AST_TYPE_ARRAY: ast_type → nat → ast_type
+| AST_TYPE_STRUCT: ne_list ast_type → ast_type.
+
+(* principio di eliminazione arricchito *)
+nlet rec ast_type_index_aux (P:ast_type → Prop)
+                            (f:Πt.P t → P (AST_TYPE_STRUCT (ne_nil ? t)))
+                            (f1:Πh,t.P h → P (AST_TYPE_STRUCT t) → P (AST_TYPE_STRUCT (ne_cons ? h t)))
+                            (f2:Πt.P t)
+                            (t:ne_list ast_type) on t ≝
+ match t return λt.P (AST_TYPE_STRUCT t) with
+  [ ne_nil h ⇒ f h (f2 h)
+  | ne_cons h t ⇒ f1 h t (f2 h) (ast_type_index_aux P f f1 f2 t)
+  ].
+
+nlet rec ast_type_index (P:ast_type → Prop)
+                        (f:Πb.P (AST_TYPE_BASE b))
+                        (f1:Πt,n.P t → P (AST_TYPE_ARRAY t n))
+                        (f2:Πt.P t → P (AST_TYPE_STRUCT (ne_nil ? t)))
+                        (f3:Πh,t.P h → P (AST_TYPE_STRUCT t) → P (AST_TYPE_STRUCT (ne_cons ? h t)))
+                        (t:ast_type) on t : P t ≝
+ match t return λt.P t with
+  [ AST_TYPE_BASE b ⇒ f b
+  | AST_TYPE_ARRAY t' n ⇒ f1 t' n (ast_type_index P f f1 f2 f3 t')
+  | AST_TYPE_STRUCT nl ⇒ match nl with
+   [ ne_nil h ⇒ f2 h (ast_type_index P f f1 f2 f3 h)
+   | ne_cons h t ⇒ f3 h t (ast_type_index P f f1 f2 f3 h) (ast_type_index_aux P f2 f3 (ast_type_index P f f1 f2 f3) t)
+   ]
+  ]. 
+
+nlet rec ast_type_rectex_aux (P:ast_type → Type)
+                             (f:Πt.P t → P (AST_TYPE_STRUCT (ne_nil ? t)))
+                             (f1:Πh,t.P h → P (AST_TYPE_STRUCT t) → P (AST_TYPE_STRUCT (ne_cons ? h t)))
+                             (f2:Πt.P t)
+                             (t:ne_list ast_type) on t ≝
+ match t return λt.P (AST_TYPE_STRUCT t) with
+  [ ne_nil h ⇒ f h (f2 h)
+  | ne_cons h t ⇒ f1 h t (f2 h) (ast_type_rectex_aux P f f1 f2 t)
+  ].
+
+nlet rec ast_type_rectex (P:ast_type → Type)
+                         (f:Πb.P (AST_TYPE_BASE b))
+                         (f1:Πt,n.P t → P (AST_TYPE_ARRAY t n))
+                         (f2:Πt.P t → P (AST_TYPE_STRUCT (ne_nil ? t)))
+                         (f3:Πh,t.P h → P (AST_TYPE_STRUCT t) → P (AST_TYPE_STRUCT (ne_cons ? h t)))
+                         (t:ast_type) on t : P t ≝
+ match t return λt.P t with
+  [ AST_TYPE_BASE b ⇒ f b
+  | AST_TYPE_ARRAY t' n ⇒ f1 t' n (ast_type_rectex P f f1 f2 f3 t')
+  | AST_TYPE_STRUCT nl ⇒ match nl with
+   [ ne_nil h ⇒ f2 h (ast_type_rectex P f f1 f2 f3 h)
+   | ne_cons h t ⇒ f3 h t (ast_type_rectex P f f1 f2 f3 h) (ast_type_rectex_aux P f2 f3 (ast_type_rectex P f f1 f2 f3) t)
+   ]
+  ]. 
+
+ndefinition eq_ast_base_type ≝
+λt1,t2:ast_base_type.match t1 with
+ [ AST_BASE_TYPE_BYTE8 ⇒ match t2 with
+  [ AST_BASE_TYPE_BYTE8 ⇒ true | _ ⇒ false ]
+ | AST_BASE_TYPE_WORD16 ⇒ match t2 with
+  [ AST_BASE_TYPE_WORD16 ⇒ true | _ ⇒ false ]
+ | AST_BASE_TYPE_WORD32 ⇒ match t2 with
+  [ AST_BASE_TYPE_WORD32 ⇒ true | _ ⇒ false ]
+ ].
+
+nlet rec eq_ast_type (t1,t2:ast_type) on t1 ≝
+ match t1 with
+  [ AST_TYPE_BASE bType1 ⇒ match t2 with
+   [ AST_TYPE_BASE bType2 ⇒ eq_ast_base_type bType1 bType2
+   | _ ⇒ false ]
+  | AST_TYPE_ARRAY subType1 dim1 ⇒ match t2 with
+   [ AST_TYPE_ARRAY subType2 dim2 ⇒ (eq_ast_type subType1 subType2) ⊗ (eq_nat dim1 dim2)
+   | _ ⇒ false ]
+  | AST_TYPE_STRUCT nelSubType1 ⇒ match t2 with
+   [ AST_TYPE_STRUCT nelSubType2 ⇒ bfold_right_neList2 ? (λx1,x2.eq_ast_type x1 x2) nelSubType1 nelSubType2
+   | _ ⇒ false
+   ]
+  ].
+
+ndefinition is_ast_base_type ≝
+λast:ast_type.match ast with [ AST_TYPE_BASE _ ⇒ True | _ ⇒ False ].
+
+ndefinition isb_ast_base_type ≝
+λast:ast_type.match ast with [ AST_TYPE_BASE _ ⇒ true | _ ⇒ false ].
+
+ndefinition isnt_ast_base_type ≝
+λast:ast_type.match ast with [ AST_TYPE_BASE _ ⇒ False | _ ⇒ True ].
+
+ndefinition isntb_ast_base_type ≝
+λast:ast_type.match ast with [ AST_TYPE_BASE _ ⇒ false | _ ⇒ true ].
+
+ndefinition eval_size_base_type ≝
+λast:ast_base_type.match ast with
+ [ AST_BASE_TYPE_BYTE8 ⇒ 1
+ | AST_BASE_TYPE_WORD16 ⇒ 2
+ | AST_BASE_TYPE_WORD32 ⇒ 4
+ ].
+
+nlet rec eval_size_type (ast:ast_type) on ast ≝
+ match ast with
+  [ AST_TYPE_BASE b ⇒ eval_size_base_type b
+  | AST_TYPE_ARRAY sub_ast dim ⇒ (dim+1)*(eval_size_type sub_ast)
+  | AST_TYPE_STRUCT nel_ast ⇒ fold_right_neList … (λt,x.(eval_size_type t)+x) O nel_ast
+  ].
diff --git a/helm/software/matita/contribs/ng_assembly/compiler/ast_type_lemmas.ma b/helm/software/matita/contribs/ng_assembly/compiler/ast_type_lemmas.ma
new file mode 100755
index 000000000..7a257f335
--- /dev/null
+++ b/helm/software/matita/contribs/ng_assembly/compiler/ast_type_lemmas.ma
@@ -0,0 +1,322 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Cosimo Oliboni, oliboni@cs.unibo.it                   *)
+(*     Cosimo Oliboni, oliboni@cs.unibo.it                                *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "compiler/ast_type.ma".
+include "common/list_utility_lemmas.ma".
+
+(* ************************* *)
+(* dimensioni degli elementi *)
+(* ************************* *)
+
+ndefinition astbasetype_destruct_aux ≝
+Πb1,b2:ast_base_type.ΠP:Prop.b1 = b2 →
+ match b1 with
+  [ AST_BASE_TYPE_BYTE8 ⇒ match b2 with [ AST_BASE_TYPE_BYTE8 ⇒ P → P | _ ⇒ P ]
+  | AST_BASE_TYPE_WORD16 ⇒ match b2 with [ AST_BASE_TYPE_WORD16 ⇒ P → P | _ ⇒ P ]
+  | AST_BASE_TYPE_WORD32 ⇒ match b2 with [ AST_BASE_TYPE_WORD32 ⇒ P → P | _ ⇒ P ]
+  ].
+
+ndefinition astbasetype_destruct : astbasetype_destruct_aux.
+ #b1; #b2; #P;
+ nelim b1;
+ nelim b2;
+ nnormalize;
+ #H;
+ ##[ ##1,5,9: napply (λx:P.x)
+ ##| ##2,3: napply False_ind;
+            nchange with (match AST_BASE_TYPE_BYTE8 with [ AST_BASE_TYPE_BYTE8 ⇒ False | _ ⇒ True]);
+            nrewrite > H;
+            nnormalize;
+            napply I
+ ##| ##4,6: napply False_ind;
+            nchange with (match AST_BASE_TYPE_WORD16 with [ AST_BASE_TYPE_WORD16 ⇒ False | _ ⇒ True]);
+            nrewrite > H;
+            nnormalize;
+            napply I
+ ##| ##7,8: napply False_ind;
+            nchange with (match AST_BASE_TYPE_WORD32 with [ AST_BASE_TYPE_WORD32 ⇒ False | _ ⇒ True]);
+            nrewrite > H;
+            nnormalize;
+            napply I
+ ##]
+nqed.
+
+nlemma symmetric_eqastbasetype : symmetricT ast_base_type bool eq_ast_base_type.
+ #b1; #b2; ncases b1; ncases b2; nnormalize; napply refl_eq. nqed.
+
+nlemma eqastbasetype_to_eq : ∀b1,b2.eq_ast_base_type b1 b2 = true → b1 = b2.
+ #b1; #b2; ncases b1; ncases b2; nnormalize;
+ ##[ ##1,5,9: #H; napply refl_eq
+ ##| ##*: #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma eq_to_eqastbasetype : ∀b1,b2.b1 = b2 → eq_ast_base_type b1 b2 = true.
+ #b1; #b2; ncases b1; ncases b2; nnormalize;
+ ##[ ##1,5,9: #H; napply refl_eq
+ ##| ##*: #H; napply (astbasetype_destruct … H)
+ ##]
+nqed.
+
+nlemma asttype_destruct_base_base : ∀b1,b2.AST_TYPE_BASE b1 = AST_TYPE_BASE b2 → b1 = b2.
+ #b1; #b2; #H;
+ nchange with (match AST_TYPE_BASE b2 with [ AST_TYPE_BASE a ⇒ b1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma asttype_destruct_array_array_1 : ∀x1,x2,y1,y2.AST_TYPE_ARRAY x1 y1 = AST_TYPE_ARRAY x2 y2 → x1 = x2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match AST_TYPE_ARRAY x2 y2 with [ AST_TYPE_ARRAY a _ ⇒ x1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma asttype_destruct_array_array_2 : ∀x1,x2,y1,y2.AST_TYPE_ARRAY x1 y1 = AST_TYPE_ARRAY x2 y2 → y1 = y2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match AST_TYPE_ARRAY x2 y2 with [ AST_TYPE_ARRAY _ b ⇒ y1 = b | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma asttype_destruct_struct_struct : ∀b1,b2.AST_TYPE_STRUCT b1 = AST_TYPE_STRUCT b2 → b1 = b2.
+ #b1; #b2; #H;
+ nchange with (match AST_TYPE_STRUCT b2 with [ AST_TYPE_STRUCT a ⇒ b1 = a | _ ⇒ False ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+ndefinition asttype_destruct_aux ≝
+Πb1,b2:ast_type.ΠP:Prop.b1 = b2 →
+ match b1 with
+  [ AST_TYPE_BASE s1 ⇒ match b2 with
+   [ AST_TYPE_BASE s2 ⇒ match s1 with
+    [ AST_BASE_TYPE_BYTE8 ⇒ match s2 with [ AST_BASE_TYPE_BYTE8 ⇒ P → P | _ ⇒ P ]
+    | AST_BASE_TYPE_WORD16 ⇒ match s2 with [ AST_BASE_TYPE_WORD16 ⇒ P → P | _ ⇒ P ]
+    | AST_BASE_TYPE_WORD32 ⇒ match s2 with [ AST_BASE_TYPE_WORD32 ⇒ P → P | _ ⇒ P ]
+    ] | _ ⇒ P ]
+  | AST_TYPE_ARRAY _ _ ⇒ match b2 with [ AST_TYPE_ARRAY _ _ ⇒ P → P | _ ⇒ P ]
+  | AST_TYPE_STRUCT _ ⇒ match b2 with [ AST_TYPE_STRUCT _ ⇒ P → P | _ ⇒ P ]
+  ].
+
+ndefinition asttype_destruct : asttype_destruct_aux.
+ #b1; #b2; #P;
+ ncases b1;
+ ##[ ##1: ncases b2;
+          ##[ ##1: nnormalize; #s1; #s2; ncases s1; ncases s2; nnormalize;
+                   ##[ ##1,5,9: #H; napply (λx:P.x)
+                   ##| ##*: #H; napply (astbasetype_destruct … (asttype_destruct_base_base … H))
+                   ##]
+          ##| ##2: #t; #n; #b; nnormalize; #H
+          ##| ##3: #l; #b; nnormalize; #H
+          ##]
+          napply False_ind;
+          nchange with (match AST_TYPE_BASE b with [ AST_TYPE_BASE _ ⇒ False | _ ⇒ True ]);
+          nrewrite > H; nnormalize; napply I
+ ##| ##2: ncases b2;
+          ##[ ##2: #t1; #n1; #t2; #n2; nnormalize; #H; napply (λx:P.x)
+          ##| ##1: #b; #t; #n; nnormalize; #H
+          ##| ##3: #l; #t; #n; nnormalize; #H
+          ##]
+          napply False_ind;
+          nchange with (match AST_TYPE_ARRAY t n with [ AST_TYPE_ARRAY _ _ ⇒ False | _ ⇒ True ]);
+          nrewrite > H; nnormalize; napply I
+ ##| ##3: ncases b2;
+          ##[ ##3: #l1; #l2; nnormalize; #H; napply (λx:P.x)
+          ##| ##1: #b; #l; nnormalize; #H
+          ##| ##2: #t; #n; #l; nnormalize; #H
+          ##]
+          napply False_ind;
+          nchange with (match AST_TYPE_STRUCT l with [ AST_TYPE_STRUCT _ ⇒ False | _ ⇒ True ]);
+          nrewrite > H; nnormalize; napply I
+ ##]
+nqed.
+
+nlemma symmetric_eqasttype_aux1
+ : ∀nl1,nl2.
+  (eq_ast_type (AST_TYPE_STRUCT nl1) (AST_TYPE_STRUCT nl2)) = (eq_ast_type (AST_TYPE_STRUCT nl2) (AST_TYPE_STRUCT nl1)) →
+  (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl1 nl2) = (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl2 nl1).
+ #nl1; #nl2; #H;
+ napply H.
+nqed.
+
+nlemma symmetric_eqasttype : symmetricT ast_type bool eq_ast_type.
+ #t1; napply (ast_type_index … t1);
+ ##[ ##1: #b1; #t2; ncases t2;
+          ##[ ##1: #b2; nchange with ((eq_ast_base_type b1 b2) = (eq_ast_base_type b2 b1));
+                   nrewrite > (symmetric_eqastbasetype b1 b2);
+                   napply refl_eq
+          ##| ##2: #st2; #n2; nnormalize; napply refl_eq
+          ##| ##3: #nl2; nnormalize; napply refl_eq
+          ##]
+ ##| ##2: #st1; #n1; #H; #t2; ncases t2;
+          ##[ ##2: #st2; #n2; nchange with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = ((eq_ast_type st2 st1)⊗(eq_nat n2 n1)));
+                   nrewrite > (symmetric_eqnat n1 n2);
+                   nrewrite > (H st2);
+                   napply refl_eq
+          ##| ##1: #b2; nnormalize; napply refl_eq
+          ##| ##3: #nl2; nnormalize; napply refl_eq
+          ##]
+ ##| ##3: #hh1; #H; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; nchange with ((eq_ast_type hh1 hh2) = (eq_ast_type hh2 hh1));
+                            nrewrite > (H hh2);
+                            napply refl_eq
+                   ##| ##2: #hh2; #ll2; nnormalize; napply refl_eq
+                   ##]
+          ##| ##1: #b2; nnormalize; napply refl_eq
+          ##| ##2: #st2; #n2; nnormalize; napply refl_eq
+          ##]
+ ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; nnormalize; napply refl_eq
+                   ##| ##2: #hh2; #ll2; nnormalize;
+                            nrewrite > (H hh2);
+                            nrewrite > (symmetric_eqasttype_aux1 ll1 ll2 (H1 (AST_TYPE_STRUCT ll2)));
+                            napply refl_eq
+                   ##]
+          ##| ##1: #b2; nnormalize; napply refl_eq
+          ##| ##2: #st2; #n2; nnormalize; napply refl_eq
+          ##]
+ ##]
+nqed.
+
+nlemma eqasttype_to_eq : ∀t1,t2.eq_ast_type t1 t2 = true → t1 = t2.
+ #t1;
+ napply (ast_type_index … t1);
+ ##[ ##1: #b1; #t2; ncases t2;
+          ##[ ##1: #b2; #H; nchange in H:(%) with ((eq_ast_base_type b1 b2) = true);
+                   nrewrite > (eqastbasetype_to_eq b1 b2 H);
+                   napply refl_eq
+          ##| ##2: #st2; #n2; nnormalize; #H; napply (bool_destruct … H)
+          ##| ##3: #nl2; nnormalize; #H; napply (bool_destruct … H)
+          ##]
+ ##| ##2: #st1; #n1; #H; #t2; ncases t2;
+          ##[ ##2: #st2; #n2; #H1; nchange in H1:(%) with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = true);
+                   nrewrite > (H st2 (andb_true_true_l … H1));
+                   nrewrite > (eqnat_to_eq n1 n2 (andb_true_true_r … H1));
+                   napply refl_eq
+          ##| ##1: #b2; nnormalize; #H1; napply (bool_destruct … H1)
+          ##| ##3: #nl2; nnormalize; #H1; napply (bool_destruct … H1)
+          ##]
+ ##| ##3: #hh1; #H; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; #H1; nchange in H1:(%) with ((eq_ast_type hh1 hh2) = true);
+                            nrewrite > (H hh2 H1);
+                            napply refl_eq
+                   ##| ##2: #hh2; #ll2; nnormalize; #H1; napply (bool_destruct … H1)
+                   ##]
+          ##| ##1: #b2; nnormalize; #H1; napply (bool_destruct … H1)
+          ##| ##2: #st2; #n2; nnormalize; #H1; napply (bool_destruct … H1)
+          ##]
+ ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; nnormalize; #H2; napply (bool_destruct … H2)
+                   ##| ##2: #hh2; #ll2; #H2; nchange in H2:(%) with (((eq_ast_type hh1 hh2)⊗(bfold_right_neList2 ? (λx,y.eq_ast_type x y) ll1 ll2)) = true);
+                            nrewrite > (H hh2 (andb_true_true_l … H2));
+                            nrewrite > (asttype_destruct_struct_struct ll1 ll2 (H1 (AST_TYPE_STRUCT ll2) (andb_true_true_r … H2)));
+                            napply refl_eq
+                   ##]
+          ##| ##1: #b2; nnormalize; #H2; napply (bool_destruct … H2)
+          ##| ##2: #st2; #n2; nnormalize; #H2; napply (bool_destruct … H2)
+          ##]
+ ##]
+nqed.
+
+nlemma eq_to_eqasttype_aux1
+ : ∀nl1,nl2.
+  ((eq_ast_type (AST_TYPE_STRUCT nl1) (AST_TYPE_STRUCT nl2)) = true) →
+  ((bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl1 nl2) = true).
+ #nl1; #nl2; #H;
+ napply H.
+nqed.
+
+nlemma eq_to_eqasttype : ∀t1,t2.t1 = t2 → eq_ast_type t1 t2 = true.
+ #t1;
+ napply (ast_type_index … t1);
+ ##[ ##1: #b1; #t2; ncases t2;
+          ##[ ##1: #b2; #H; nrewrite > (asttype_destruct_base_base … H);
+                   nchange with ((eq_ast_base_type b2 b2) = true);
+                   nrewrite > (eq_to_eqastbasetype b2 b2 (refl_eq …));
+                   napply refl_eq
+          ##| ##2: #st2; #n2; #H; napply (asttype_destruct … H)
+          ##| ##3: #nl2; #H; napply (asttype_destruct … H)
+          ##]
+ ##| ##2: #st1; #n1; #H; #t2; ncases t2;
+          ##[ ##2: #st2; #n2; #H1;  nchange with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = true);
+                   nrewrite > (H st2 (asttype_destruct_array_array_1 … H1));
+                   nrewrite > (eq_to_eqnat n1 n2 (asttype_destruct_array_array_2 … H1));
+                   nnormalize;
+                   napply refl_eq
+          ##| ##1: #b2; #H1; napply (asttype_destruct … H1)
+          ##| ##3: #nl2; #H1; napply (asttype_destruct … H1)
+          ##]
+ ##| ##3: #hh1; #H; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; #H1; nchange with ((eq_ast_type hh1 hh2) = true);
+                            nrewrite > (H hh2 (nelist_destruct_nil_nil ? hh1 hh2 (asttype_destruct_struct_struct … H1)));
+                            napply refl_eq
+                   ##| ##2: #hh2; #ll2; #H1; nelim (nelist_destruct_nil_cons ? hh1 hh2 ll2 (asttype_destruct_struct_struct … H1))
+                   ##]
+          ##| ##1: #b2; #H1; napply (asttype_destruct … H1)
+          ##| ##2: #st2; #n2; #H1; napply (asttype_destruct … H1)
+          ##]
+ ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
+          ##[ ##3: #nl2; ncases nl2;
+                   ##[ ##1: #hh2; #H2; nelim (nelist_destruct_cons_nil ? hh1 hh2 ll1 (asttype_destruct_struct_struct … H2))
+                   ##| ##2: #hh2; #ll2; #H2; nchange with (((eq_ast_type hh1 hh2)⊗(bfold_right_neList2 ? (λx,y.eq_ast_type x y) ll1 ll2)) = true);
+                            nrewrite > (H hh2 (nelist_destruct_cons_cons_1 … (asttype_destruct_struct_struct … H2)));
+                            nrewrite > (eq_to_eqasttype_aux1 ll1 ll2 (H1 (AST_TYPE_STRUCT ll2) ?));
+                            ##[ ##1: nnormalize; napply refl_eq
+                            ##| ##2: nrewrite > (nelist_destruct_cons_cons_2 … (asttype_destruct_struct_struct … H2));
+                                     napply refl_eq
+                            ##]
+                   ##]
+          ##| ##1: #b2; #H2; napply (asttype_destruct … H2)
+          ##| ##2: #st2; #n2; #H2; napply (asttype_destruct … H2)
+          ##]
+ ##]
+nqed.
+
+nlemma isbastbasetype_to_isastbasetype : ∀ast.isb_ast_base_type ast = true → is_ast_base_type ast.
+ #ast;
+ ncases ast;
+ nnormalize;
+ ##[ ##1: #t; #H; napply I
+ ##| ##2: #t; #n; #H; napply (bool_destruct … H)
+ ##| ##3: #t; #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma isntbastbasetype_to_isntastbasetype : ∀ast.isntb_ast_base_type ast = true → isnt_ast_base_type ast.
+ #ast;
+ ncases ast;
+ nnormalize;
+ ##[ ##1: #t; #H; napply (bool_destruct … H)
+ ##| ##2: #t; #n; #H; napply I
+ ##| ##3: #l; #H; napply I
+ ##]
+nqed.
diff --git a/helm/software/matita/contribs/ng_assembly/depends b/helm/software/matita/contribs/ng_assembly/depends
index 86f3a5619..943772164 100644
--- a/helm/software/matita/contribs/ng_assembly/depends
+++ b/helm/software/matita/contribs/ng_assembly/depends
@@ -11,6 +11,7 @@ common/nat.ma num/bool.ma
 freescale/opcode_base_lemmas.ma freescale/opcode_base.ma num/bool_lemmas.ma
 freescale_tests/medium_tests_tools.ma freescale/multivm.ma
 common/string_lemmas.ma common/ascii_lemmas2.ma common/list_utility_lemmas.ma common/string.ma
+compiler/ast_type_lemmas.ma common/list_utility_lemmas.ma compiler/ast_type.ma
 num/quatern.ma num/bool.ma
 freescale/table_HC05_tests.ma freescale/opcode.ma freescale/table_HC05.ma
 num/exadecim.ma common/nat.ma common/prod.ma num/bool.ma num/oct.ma num/quatern.ma
@@ -26,12 +27,13 @@ freescale/table_RS08_tests.ma freescale/opcode.ma freescale/table_RS08.ma
 freescale/translation.ma common/option.ma freescale/table_HC05.ma freescale/table_HC08.ma freescale/table_HCS08.ma freescale/table_RS08.ma
 freescale/memory_abs.ma freescale/memory_bits.ma freescale/memory_func.ma freescale/memory_trees.ma
 num/word32_lemmas.ma num/word16_lemmas.ma num/word32.ma
-test_errori.ma 
+test_errori.ma num/exadecim.ma num/exadecim_lemmas.ma
 freescale/memory_struct.ma num/byte8.ma num/oct.ma
 freescale/model.ma freescale/status.ma
 freescale/table_HC05.ma common/list.ma freescale/opcode_base.ma
 common/string.ma common/ascii.ma common/list_utility.ma
 common/theory.ma 
+compiler/ast_type.ma common/list_utility.ma
 num/word16.ma num/byte8.ma
 freescale/memory_trees.ma common/list.ma common/option.ma freescale/memory_struct.ma num/word16.ma
 common/prod.ma num/bool.ma
diff --git a/helm/software/matita/contribs/ng_assembly/test_errori.ma b/helm/software/matita/contribs/ng_assembly/test_errori.ma
index 4236c5c63..921c1b505 100644
--- a/helm/software/matita/contribs/ng_assembly/test_errori.ma
+++ b/helm/software/matita/contribs/ng_assembly/test_errori.ma
@@ -1,4 +1,28 @@
 
+(* congettura, come si fa? *)
+include "num/exadecim.ma".
+include "num/exadecim_lemmas.ma".
+
+nlemma decidable_ex_aux1 : ∀x.∀H:x0 = x.(x0 = x) ∨ (x0 ≠ x).
+ #x; nelim x;
+ ##[ ##1: #H; napply (or_introl … H)
+ ##| ##*: #H; nelim (exadecim_destruct … H)
+ ##]. nqed.
+
+nlemma decidable_ex0 : ∀x:exadecim.decidable (x0 = x).
+ #x;
+ nelim x;
+ nnormalize;
+ napply (Or_ind (x0=x) (x0≠x) ? ? …);
+ ##[ ##1: napply (or_introl (x0 = x0) (x0 ≠ x0) (refl_eq …))
+ ##| ##*:
+ 
+ nnormalize;
+ nelim x;
+ ##[ ##1: nelim y;
+          ##[ ##1: napply (or_introl (? = ?) (? ≠ ?) (refl_eq …))
+          ##| ##*:
+
 (*include "utility/utility.ma".
 
 nlemma fold_right_neList2_aux3 :