propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / nat_pred_succ.ma

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 b7f9918b08d0191cf52391c310700d278be31116..dafe179103c40e47e1826004af3b277d07961bd2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
+++ b/matita/matita/contribs/lambdadelta/ground/arith/nat_pred_succ.ma
@@ -17,6 +17,21 @@ include "ground/arith/nat_pred.ma".
 
 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
 
+(* Constructions with npsucc ************************************************)
+
+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 *)
@@ -24,7 +39,7 @@ lemma npred_succ (n): n = ↓↑n.
 * //
 qed.
 
-(* Inversion with nsucc *****************************************************)
+(* Inversions with nsucc ****************************************************)
 
 (*** nat_split *)
 lemma nat_split_zero_pos (n): ∨∨ 𝟎 = n | n = ↑↓n.