X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred_succ.ma;h=3d79e371ebb0561e12510868a5af77df236c3868;hb=4d232392091ee233afc26ecf3120dd5f5c6a33c8;hp=71e5e921fd48558b7f890ba5b3bdfdddeabafcc2;hpb=74c6905907b0bca229366d52450e2a6982b5b8be;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 71e5e921f..3d79e371e 100644
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
@@ -15,11 +15,19 @@
 include "ground/arith/nat_succ.ma".
 include "ground/arith/nat_pred.ma".
 
-(* NON-NEGATIVE INTEGERS ****************************************************)
+(* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
 
-(* Basic rewrites with succ *************************************************)
+(* Constructions with nsucc *************************************************)
 
-(*** pred_Sn *)
+(*** pred_Sn pred_S *)
 lemma npred_succ (n): n = ↓↑n.
 * //
 qed.
+
+(* Inversions 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-.