X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fassembly%2Ffreescale%2Fextra.ma;h=7da45c848e3a2aef8e3f012548998ea217c177ce;hb=6ee4fa0ba5f4b6601b62afd482d4f30bd2de2f91;hp=25e0cb6fab5fe0f00cb7edf9d5d6419d9ce63fc3;hpb=f2d9db85559c7a8db11aae1153495fae4a258d54;p=helm.git

diff --git a/helm/software/matita/contribs/assembly/freescale/extra.ma b/helm/software/matita/contribs/assembly/freescale/extra.ma
index 25e0cb6fa..7da45c848 100644
--- a/helm/software/matita/contribs/assembly/freescale/extra.ma
+++ b/helm/software/matita/contribs/assembly/freescale/extra.ma
@@ -54,6 +54,51 @@ 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;
@@ -64,6 +109,16 @@ lemma eqbool_to_eq : ∀b1,b2:bool.(eq_bool b1 b2 = true) → (b1 = b2).
  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 }.
@@ -153,7 +208,7 @@ axiom or_lt_le : ∀n,m. n < m ∨ m ≤ n.
 
 lemma le_to_lt: ∀n,m. n ≤ m → n < S m.
  intros;
- autobatch.
+ unfold;autobatch.
 qed.
 
 alias num (instance 0) = "natural number".
@@ -198,7 +253,7 @@ lemma leq_m_n_to_eq_div_n_m_S: ∀n,m:nat. 0 < m → m ≤ n → ∃z. n/m = S z
         ]
      | elim H1; autobatch
      ]
-  | autobatch
+  | exists;[apply (pred m);]autobatch
   ].
 qed.