<tr_xap_unfold <tr_xap_unfold
/3 width=1 by tr_push_eq_repl, tr_nap_eq_repl/
qed.
+
+lemma tr_nap_plus (f) (m) (n):
+ ⇂*[↑n]f@❨m❩+f@§❨n❩ = f@§❨m+n❩.
+/2 width=1 by eq_inv_nsucc_bi/
+qed.
+
+lemma tr_xap_pos (f) (n):
+ n = ↑↓n → f@❨n❩=↑↓(f@❨n❩).
+#f #n #H0 >H0 -H0
+<tr_xap_ninj <nsucc_pnpred //
+qed.