freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / common / string_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/common/string_lemmas.ma b/helm/software/matita/contribs/ng_assembly/common/string_lemmas.ma
new file mode 100755 (executable)
index 0000000..67590ae
--- /dev/null
+++ b/helm/software/matita/contribs/ng_assembly/common/string_lemmas.ma
@@ -0,0 +1,101 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/string.ma".
+include "common/ascii_lemmas2.ma".
+include "common/list_utility_lemmas.ma".
+
+(* ************************ *)
+(* MANIPOLAZIONE DI STRINGA *)
+(* ************************ *)
+
+nlemma symmetric_eqstr : symmetricT (list ascii) bool eq_str.
+ #s1; #s2;
+ napply (symmetric_bfoldrightlist2 ascii eq_ascii s1 s2 symmetric_eqascii).
+nqed.
+
+nlemma eqstr_to_eq : ∀s,s'.eq_str s s' = true → s = s'.
+ #s1; #s2;
+ napply (bfoldrightlist2_to_eq ascii eq_ascii s1 s2 eqascii_to_eq).
+nqed.
+
+nlemma eq_to_eqstr : ∀s,s'.s = s' → eq_str s s' = true.
+ #s1; #s2;
+ napply (eq_to_bfoldrightlist2 ascii eq_ascii s1 s2 eq_to_eqascii).
+nqed.
+
+(* ************ *)
+(* STRINGA + ID *)
+(* ************ *)
+
+nlemma strid_destruct_1 : ∀x1,x2,y1,y2.mk_strId x1 y1 = mk_strId x2 y2 → x1 = x2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match mk_strId x2 y2 with [ mk_strId a _ ⇒ x1 = a ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma strid_destruct_2 : ∀x1,x2,y1,y2.mk_strId x1 y1 = mk_strId x2 y2 → y1 = y2.
+ #x1; #x2; #y1; #y2; #H;
+ nchange with (match mk_strId x2 y2 with [ mk_strId _ b ⇒ y1 = b ]);
+ nrewrite < H;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma symmetric_eqstrid : symmetricT strId bool eq_strId.
+ #si1; #si2;
+ nchange with (
+  ((eq_str (str_elem si1) (str_elem si2))⊗(eq_nat (id_elem si1) (id_elem si2))) =
+  ((eq_str (str_elem si2) (str_elem si1))⊗(eq_nat (id_elem si2) (id_elem si1))));
+ nrewrite > (symmetric_eqstr (str_elem si1) (str_elem si2));
+ nrewrite > (symmetric_eqnat (id_elem si1) (id_elem si2));
+ napply refl_eq.
+nqed. 
+
+nlemma eqstrid_to_eq : ∀s,s'.eq_strId s s' = true → s = s'.
+ #si1; #si2;
+ nelim si1;
+ #l1; #n1;
+ nelim si2;
+ #l2; #n2; #H;
+ nchange in H:(%) with (((eq_str l1 l2)⊗(eq_nat n1 n2)) = true);
+ nrewrite > (eqstr_to_eq l1 l2 (andb_true_true_l … H));
+ nrewrite > (eqnat_to_eq n1 n2 (andb_true_true_r … H));
+ napply refl_eq.
+nqed.
+
+nlemma eq_to_eqstrid : ∀s,s'.s = s' → eq_strId s s' = true.
+ #si1; #si2;
+ nelim si1;
+ #l1; #n1;
+ nelim si2;
+ #l2; #n2; #H;
+ nchange with (((eq_str l1 l2)⊗(eq_nat n1 n2)) = true);
+ nrewrite > (strid_destruct_1 … H);
+ nrewrite > (strid_destruct_2 … H);
+ nrewrite > (eq_to_eqstr l2 l2 (refl_eq …));
+ nrewrite > (eq_to_eqnat n2 n2 (refl_eq …));
+ nnormalize;
+ napply refl_eq.
+nqed.