X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fpnat.ma;h=516ba683a1687802780fa3b7eba0724612941562;hp=d90f8dd8d23ec00b536a5db1aeb06221aa0ab20d;hb=8fdf1af656038d0245eba64ff2531bbe94ce0e9e;hpb=77c9255de3c5f7780aeacd745703a1cc76328a68

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/pnat.ma b/matita/matita/contribs/lambdadelta/ground/arith/pnat.ma
index d90f8dd8d..516ba683a 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/pnat.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/pnat.ma
@@ -55,3 +55,14 @@ lemma eq_pnat_dec (p1,p2:pnat): Decidable (p1 = p2).
 | /2 width=1 by or_introl/
 ]
 qed-.
+
+(* Basic eliminations *******************************************************)
+
+lemma pnat_ind_2 (Q:relation2 …):
+      (∀q. Q (𝟏) q) →
+      (∀p. Q p (𝟏) → Q (↑p) (𝟏)) →
+      (∀p,q. Q p q → Q (↑p) (↑q)) →
+      ∀p,q. Q p q.
+#Q #IH1 #IH2 #IH3 #p elim p -p [ // ]
+#p #IH #q elim q -q /2 width=1 by/
+qed-.