X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Flib%2Flist_append.ma;h=6b5eb992a7b64e5c932ff950b8ca00f4b8a7e29c;hb=e6ef5581641345f1c5c72f3c8b6040a9c6e5aecb;hp=31644956669dea1ade08a8e62593873695736452;hpb=513a56a5990201abcf038e7242779e2d73621c86;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/list_append.ma b/matita/matita/contribs/lambdadelta/ground/lib/list_append.ma
index 316449566..6b5eb992a 100644
--- a/matita/matita/contribs/lambdadelta/ground/lib/list_append.ma
+++ b/matita/matita/contribs/lambdadelta/ground/lib/list_append.ma
@@ -68,6 +68,24 @@ lemma eq_inv_list_empty_append (A):
 ]
 qed-.
 
+lemma eq_inv_list_append_empty (A):
+      ∀l1,l2. l1⨁{A}l2 = ⓔ →
+      ∧∧ l1 = ⓔ & l2 = ⓔ.
+#A *
+[ #l2 /2 width=1 by conj/
+| #a1 #l1 #l2 <list_append_lcons_sn #H destruct
+]
+qed-.
+
+(* Advanced inversions ******************************************************)
+
+lemma eq_inv_list_append_dx_sn_refl (A) (l1) (l2):
+      l1 = l1⨁{A}l2 → ⓔ = l2.
+#A #l1 elim l1 -l1 [ // ]
+#a1 #l1 #IH #l2 <list_append_lcons_sn #H0 destruct -H0
+/2 width=1 by/
+qed-.
+
 (* Advanced eliminations ****************************************************)
 
 lemma list_ind_append_dx (A) (Q:predicate …):
@@ -78,3 +96,12 @@ lemma list_ind_append_dx (A) (Q:predicate …):
 #a #l >(list_append_empty_sn … (a⨮l))
 /2 width=1 by/
 qed-.
+
+lemma list_ind_append_sn (A) (Q:predicate …):
+      Q (ⓔ{A}) →
+      (∀l1,l2. Q l2 -> Q (l1⨁l2)) →
+      ∀l. Q l.
+#A #Q #IH1 #IH2 * //
+#a #l >(list_append_empty_dx … (a⨮l))
+/2 width=1 by/
+qed-.