X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred_succ.ma;h=ac01f0f8fc3aefbf78466e018ea478e8db5840f4;hb=19b0a814861157ba05f23877d5cd94059f52c2e8;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..ac01f0f8f 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.
+
+(* Inversion with nsucc *****************************************************)
+
+(*** nat_split *)
+lemma nat_split (n): ∨∨ 𝟎 = n | n = ↑↓n.
+#n @(nat_ind_succ … n) -n
+/2 width=1 by or_introl, or_intror/
+qed-.