X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Flibrary%2Flist%2Fin.ma;h=3285fef2e0967f75a5bc601953eadba75bef148c;hb=7002fb8d9d0102e9baa410935fdabc9be0f8690d;hp=d6c165022aa1e55fc3458fe221c61597c99fa157;hpb=f48faa46342b557486e06c17fd574d1eeb386239;p=helm.git

diff --git a/helm/software/matita/library/list/in.ma b/helm/software/matita/library/list/in.ma
index d6c165022..3285fef2e 100644
--- a/helm/software/matita/library/list/in.ma
+++ b/helm/software/matita/library/list/in.ma
@@ -23,6 +23,13 @@ inductive in_list (A:Type): A → (list A) → Prop ≝
 definition incl : \forall A.(list A) \to (list A) \to Prop \def
   \lambda A,l,m.\forall x.in_list A x l \to in_list A x m.
   
+notation "hvbox(a break ∉ b)" non associative with precedence 45
+for @{ 'notmem $a $b }. 
+  
+interpretation "list member" 'mem x l = (in_list ? x l).
+interpretation "list not member" 'notmem x l = (Not (in_list ? x l)).
+interpretation "list inclusion" 'subseteq l1 l2 = (incl ? l1 l2).
+  
 lemma not_in_list_nil : \forall A,x.\lnot in_list A x [].
 intros.unfold.intro.inversion H
   [intros;lapply (sym_eq ? ? ? H2);destruct Hletin
@@ -152,4 +159,17 @@ qed.
 
 lemma incl_A_A: ∀T,A.incl T A A.
 intros.unfold incl.intros.assumption.
-qed.
\ No newline at end of file
+qed.
+
+lemma incl_append_l : ∀T,A,B.incl T A (A @ B).
+unfold incl; intros;autobatch.
+qed.
+
+lemma incl_append_r : ∀T,A,B.incl T B (A @ B).
+unfold incl; intros;autobatch.
+qed.
+
+lemma incl_cons : ∀T,A,B,x.incl T A B → incl T (x::A) (x::B).
+unfold incl; intros;elim (in_list_cons_case ? ? ? ? H1);autobatch.
+qed.
+