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 nsucc *************************************************)
-(*** pred_Sn *)
+(*** 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-.