freescale porting, work in progress

[helm.git] / helm / software / matita / contribs / ng_assembly / num / oct_lemmas.ma

diff --git a/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma b/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma
new file mode 100755 (executable)
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+++ b/helm/software/matita/contribs/ng_assembly/num/oct_lemmas.ma
@@ -0,0 +1,143 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "num/oct.ma".
+include "num/bool_lemmas.ma".
+
+(* ****** *)
+(* OTTALI *)
+(* ****** *)
+
+ndefinition oct_destruct_aux ≝
+Πn1,n2:oct.ΠP:Prop.n1 = n2 →
+ match n1 with
+  [ o0 ⇒ match n2 with [ o0 ⇒ P → P | _ ⇒ P ]
+  | o1 ⇒ match n2 with [ o1 ⇒ P → P | _ ⇒ P ]
+  | o2 ⇒ match n2 with [ o2 ⇒ P → P | _ ⇒ P ]
+  | o3 ⇒ match n2 with [ o3 ⇒ P → P | _ ⇒ P ]
+  | o4 ⇒ match n2 with [ o4 ⇒ P → P | _ ⇒ P ]
+  | o5 ⇒ match n2 with [ o5 ⇒ P → P | _ ⇒ P ]
+  | o6 ⇒ match n2 with [ o6 ⇒ P → P | _ ⇒ P ]
+  | o7 ⇒ match n2 with [ o7 ⇒ P → P | _ ⇒ P ]
+  ].
+
+ndefinition oct_destruct : oct_destruct_aux.
+ #n1; #n2; #P;
+ nelim n1;
+ ##[ ##1: nelim n2; nnormalize; #H;
+          ##[ ##1: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o0 with [ o0 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##2: nelim n2; nnormalize; #H;
+          ##[ ##2: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o1 with [ o1 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##3: nelim n2; nnormalize; #H;
+          ##[ ##3: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o2 with [ o2 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##4: nelim n2; nnormalize; #H;
+          ##[ ##4: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o3 with [ o3 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##5: nelim n2; nnormalize; #H;
+          ##[ ##5: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o4 with [ o4 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##6: nelim n2; nnormalize; #H;
+          ##[ ##6: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o5 with [ o5 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##7: nelim n2; nnormalize; #H;
+          ##[ ##7: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o6 with [ o6 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##| ##8: nelim n2; nnormalize; #H;
+          ##[ ##8: napply (λx:P.x)
+          ##| ##*: napply False_ind;
+                   nchange with (match o7 with [ o7 ⇒ False | _ ⇒ True ]);
+                   nrewrite > H; nnormalize; napply I
+          ##]
+ ##]
+nqed.
+
+nlemma symmetric_eqoct : symmetricT oct bool eq_oct.
+ #n1; #n2;
+ nelim n1;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma eqoct_to_eq : ∀n1,n2.eq_oct n1 n2 = true → n1 = n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
+ ##| ##*: #H; napply (bool_destruct … H)
+ ##]
+nqed.
+
+nlemma eq_to_eqoct : ∀n1,n2.n1 = n2 → eq_oct n1 n2 = true.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply refl_eq
+ ##| ##*: #H; napply (oct_destruct … H)
+ ##]
+nqed.
+
+nlemma neqoct_to_neq : ∀n1,n2.eq_oct n1 n2 = false → n1 ≠ n2.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply (bool_destruct … H)
+ ##| ##*: #H; #H1; napply (oct_destruct … H1)
+ ##]
+nqed.
+
+nlemma neq_to_neqoct : ∀n1,n2.n1 ≠ n2 → eq_oct n1 n2 = false.
+ #n1; #n2;
+ ncases n1;
+ ncases n2;
+ nnormalize;
+ ##[ ##1,10,19,28,37,46,55,64: #H; napply False_ind; napply (H (refl_eq …))
+ ##| ##*: #H; napply refl_eq
+ ##]
+nqed.