update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / path_proper.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
index fca2eb91aae63a0d4f1b69d459df52cc54b98e05..ff6a53c3932c4a01eac32c3e58993ab8fadb9174 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_proper.ma
@@ -30,15 +30,33 @@ interpretation
 (* Basic constructions ******************************************************)
 
 lemma ppc_lcons (l) (q): l◗q ϵ 𝐏.
-#l #p #H destruct
+#l #q #H0 destruct
+qed.
+
+lemma ppc_rcons (l) (q): q◖l ϵ 𝐏.
+#l #q #H
+elim (eq_inv_list_empty_rcons ??? H)
 qed.
 
 (* Basic inversions ********************************************************)
 
+lemma ppc_inv_empty:
+      (𝐞) ϵ 𝐏 → ⊥.
+#H0 @H0 -H0 //
+qed-.
+
 lemma ppc_inv_lcons (p):
       p ϵ 𝐏 → ∃∃l,q. l◗q = p.
 *
-[ #H elim H -H //
+[ #H0 elim (ppc_inv_empty … H0)
 | #l #q #_ /2 width=3 by ex1_2_intro/
 ]
 qed-.
+
+lemma ppc_inv_rcons (p):
+      p ϵ 𝐏 → ∃∃q,l. q◖l = p.
+#p @(list_ind_rcons … p) -p
+[ #H0 elim (ppc_inv_empty … H0)
+| #q #l #_ #_ /2 width=3 by ex1_2_intro/
+]
+qed-.