(* 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.
-(* Inversion with nsucc *****************************************************)
+(* Inversions with nsucc ****************************************************)
(*** nat_split *)
-lemma nat_split (n): ∨∨ 𝟎 = n | n = ↑↓n.
+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-.