X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fbasics%2Flogic.ma;h=8f981d46924556ee885407a1320d147ef07aaad0;hb=ef3bdc4be26f6518a82a79c64e986253f7aeaa3c;hp=2fbe45f370cb71a589d8bff1fbe1029be2ef84bc;hpb=dfb3cbe30eacd2c1b333faa3e0d92c3278c24d3c;p=helm.git

diff --git a/matita/matita/lib/basics/logic.ma b/matita/matita/lib/basics/logic.ma
index 2fbe45f37..8f981d469 100644
--- a/matita/matita/lib/basics/logic.ma
+++ b/matita/matita/lib/basics/logic.ma
@@ -30,17 +30,22 @@ lemma eq_ind_r :
 
 lemma eq_rect_Type0_r:
   ∀A.∀a.∀P: ∀x:A. eq ? x a → Type[0]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
-  #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+  #A #a #P #H #x #p lapply H lapply P
   cases p; //; qed.
-  
+
+lemma eq_rect_Type1_r:
+  ∀A.∀a.∀P: ∀x:A. eq ? x a → Type[1]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
+  #A #a #P #H #x #p lapply H lapply P
+  cases p; //; qed.
+
 lemma eq_rect_Type2_r:
   ∀A.∀a.∀P: ∀x:A. eq ? x a → Type[2]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
-  #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+  #A #a #P #H #x #p lapply H lapply P
   cases p; //; qed.
 
 lemma eq_rect_Type3_r:
   ∀A.∀a.∀P: ∀x:A. eq ? x a → Type[3]. P a (refl A a) → ∀x.∀p:eq ? x a.P x p.
-  #A #a #P #H #x #p (generalize in match H) (generalize in match P)
+  #A #a #P #H #x #p lapply H lapply P
   cases p; //; qed.
 
 theorem rewrite_l: ∀A:Type[2].∀x.∀P:A → Type[2]. P x → ∀y. x = y → P y.
@@ -148,7 +153,28 @@ inductive ex2 (A:Type[0]) (P,Q:A →Prop) : Prop ≝
 definition iff :=
  λ A,B. (A → B) ∧ (B → A).
 
-interpretation "iff" 'iff a b = (iff a b).  
+interpretation "iff" 'iff a b = (iff a b).
+
+lemma iff_sym: ∀A,B. A ↔ B → B ↔ A.
+#A #B * /3/ qed.
+
+lemma iff_trans:∀A,B,C. A ↔ B → B ↔ C → A ↔ C.
+#A #B #C * #H1 #H2 * #H3 #H4 % /3/ qed.
+
+lemma iff_not: ∀A,B. A ↔ B → ¬A ↔ ¬B.
+#A #B * #H1 #H2 % /3/ qed.
+
+lemma iff_and_l: ∀A,B,C. A ↔ B → C ∧ A ↔ C ∧ B.
+#A #B #C * #H1 #H2 % * /3/ qed.  
+
+lemma iff_and_r: ∀A,B,C. A ↔ B → A ∧ C ↔ B ∧ C.
+#A #B #C * #H1 #H2 % * /3/ qed.  
+
+lemma iff_or_l: ∀A,B,C. A ↔ B → C ∨ A ↔ C ∨ B.
+#A #B #C * #H1 #H2 % * /3/ qed.  
+
+lemma iff_or_r: ∀A,B,C. A ↔ B → A ∨ C ↔ B ∨ C.
+#A #B #C * #H1 #H2 % * /3/ qed.  
 
 (* cose per destruct: da rivedere *)