X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fground%2Farith%2Fnat_pred_succ.ma;h=4a6e23b01846b0fd7b807b095b87add5b44d060f;hb=8fe4dc148d50a0352313633bea61441bc817afbf;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..4a6e23b01 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 +15,38 @@
 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 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 *************************************************)
+
+lemma nsucc_pnpred (p):
+      ninj p = ↑(pnpred p).
+// qed.
+
+(*** 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-.