X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fassembly%2Ffreescale%2Fextra.ma;h=207a5a267d386b67af511cedf815e1c242114261;hb=026c6c5b0e094b2e6e8244909bc5ac3d88b70b9c;hp=bc76c4d6b7f0addf954b61fa572c3ad3657d803e;hpb=9eabe046c1182960de8cfdba96c5414224e3a61e;p=helm.git

diff --git a/helm/software/matita/contribs/assembly/freescale/extra.ma b/helm/software/matita/contribs/assembly/freescale/extra.ma
index bc76c4d6b..207a5a267 100644
--- a/helm/software/matita/contribs/assembly/freescale/extra.ma
+++ b/helm/software/matita/contribs/assembly/freescale/extra.ma
@@ -54,6 +54,71 @@ definition eq_bool ≝
  [ true ⇒ b2
  | false ⇒ not_bool b2 ].
 
+lemma eqbool_switch : ∀b1,b2.eq_bool b1 b2 = eq_bool b2 b1.
+ do 2 intro;
+ elim b1; elim b2;
+ reflexivity.
+qed.
+
+lemma andbool_switch : ∀b1,b2.and_bool b1 b2 = and_bool b2 b1.
+ do 2 intro;
+ elim b1; elim b2;
+ reflexivity.
+qed.
+
+lemma orbool_switch : ∀b1,b2.or_bool b1 b2 = or_bool b2 b1.
+ do 2 intro;
+ elim b1; elim b2;
+ reflexivity.
+qed.
+
+lemma xorbool_switch : ∀b1,b2.xor_bool b1 b2 = xor_bool b2 b1.
+ do 2 intro;
+ elim b1; elim b2;
+ reflexivity.
+qed.
+
+
+lemma orb_false_false :
+ ∀b1,b2:bool.((or_bool b1 b2) = false) → b1 = false.
+ intros 2;
+ elim b1 0;
+ elim b2;
+ simplify in H;
+ try destruct H;
+ reflexivity.
+qed.
+
+lemma orb_false_false_r :
+ ∀b1,b2:bool.((or_bool b1 b2) = false) → b2 = false.
+ intros 2;
+ elim b1 0;
+ elim b2;
+ simplify in H;
+ try destruct H;
+ reflexivity.
+qed.
+
+lemma eqbool_to_eq : ∀b1,b2:bool.(eq_bool b1 b2 = true) → (b1 = b2).
+ unfold eq_bool;
+ intros;
+ elim b1 in H:(%);
+ elim b2 in H:(%);
+ normalize in H:(%);
+ try reflexivity;
+ destruct H.
+qed.
+
+lemma eq_to_eqbool : ∀b1,b2.b1 = b2 → eq_bool b1 b2 = true.
+ do 2 intro;
+ elim b1 0;
+ elim b2 0;
+ intro;
+ normalize in H:(%);
+ try destruct H;
+ reflexivity.
+qed.
+
 (* \ominus *)
 notation "hvbox(⊖ a)" non associative with precedence 36
  for @{ 'not_bool $a }.