X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred_succ.ma;h=dafe179103c40e47e1826004af3b277d07961bd2;hb=7e120a2bf2e6c0882b4f4b376c5861e001945cf4;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..dafe17910 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 +17,32 @@ include "ground/arith/nat_pred.ma".
 
 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
 
-(* Rewrites with nsucc ******************************************************)
+(* Constructions with npsucc ************************************************)
 
-(*** pred_Sn *)
+lemma pnpred_succ (n): n = pnpred (npsucc n).
+* //
+qed.
+
+lemma npsucc_pred (p): p = npsucc (pnpred p).
+* //
+qed.
+
+(* Constructions with nsucc and psucc ***************************************)
+
+lemma pnpred_psucc (p): pnpred (psucc p) = nsucc (pnpred p).
+* // qed.
+
+(* Constructions with nsucc *************************************************)
+
+(*** 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-.