(* 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 *************************************************)
+lemma nsucc_pnpred (p):
+ ninj p = ↑(pnpred p).
+// qed.
+
(*** pred_Sn pred_S *)
lemma npred_succ (n): n = ↓↑n.
* //
qed.
+(* Basic inversions *********************************************************)
+
+lemma eq_inv_pnpred_bi:
+ injective … pnpred.
+#p1 #p2 #Hp
+>(npsucc_pred p1) >(npsucc_pred p2)
+<Hp -Hp @refl
+qed-.
+
(* Inversions with nsucc ****************************************************)
(*** nat_split *)