X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred_succ.ma;h=b7f9918b08d0191cf52391c310700d278be31116;hb=888840f6b3a71d3d686b53b702d362ab90ab0038;hp=26f5f9152dc5db2c9cf860c9a2116d4b91b24b44;hpb=5e72e41f4f86814e56d4b00959ccc56c71042a4c;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
index 26f5f9152..b7f9918b0 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
@@ -17,9 +17,17 @@ include "ground/arith/nat_pred.ma".
 
 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
 
-(* Rewrites with nsucc ******************************************************)
+(* Constructions with nsucc *************************************************)
 
-(*** pred_Sn *)
+(*** pred_Sn pred_S *)
 lemma npred_succ (n): n = ↓↑n.
 * //
 qed.
+
+(* Inversion with nsucc *****************************************************)
+
+(*** nat_split *)
+lemma nat_split_zero_pos (n): ∨∨ 𝟎 = n | n = ↑↓n.
+#n @(nat_ind_succ … n) -n
+/2 width=1 by or_introl, or_intror/
+qed-.